{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Multivariate Time Series forecast using seq2seq in TensorFlow\n",
    "\n",
    "This notebook implements the cast study of applying seq2seq model for time series data. \n",
    "\n",
    "The purpose is to showcase the effectiveness of seq2seq to learn the true patterns under the noisy signals. In addition, we are able to implement models with flexibility such as: \n",
    "\n",
    "- Variable input and output sequence lengths\n",
    "- Variable numbers of input and output signals \n",
    "\n",
    "This tutorial is divided into four parts - first we will be demonstrating how to train a basicseq2seq model on univariate data. The model is then easily applied to multivariate cases. We will then discuss about situation with outliers. And finally, we will showcase a real-world dataset to forecast pollution (pm2.5) in Beijing. \n",
    "\n",
    "To see the comprehensive explanations of each step, can jump to the post associated with this study - \n",
    "weiminwang.blog/2017/09/29/multivariate-time-series-forecast-using-seq2seq-in-tensorflow/\n",
    "\n",
    "This is a long notebook - you can choose the session of your interests by clicking on the links below: \n",
    "\n",
    "## Contents\n",
    "\n",
    "### 1) <b>[Univariate time series](#session1)</b> \n",
    "\n",
    "### 2) <b>[Multivariate time series](#session2)</b> \n",
    "\n",
    "### 3) <b>[Seq2seq for outliers/extreme events](#session3)</b> \n",
    "\n",
    "### 4) <b>[A case study - Beijing pollution data](#session4)</b> \n",
    "data credits go to UCI - https://archive.ics.uci.edu/ml/datasets/Beijing+PM2.5+Data"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<a id='session1'></a>\n",
    "# Univariate time series"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 259,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import tensorflow as tf\n",
    "import numpy as np \n",
    "import random\n",
    "import math\n",
    "from matplotlib import pyplot as plt\n",
    "import os\n",
    "import copy"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 260,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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kjhY+MIfoSKdpUVV0C0RrfyrF893+KwQciSkpAIXGAABfFoMZLoDCVv8AQgSI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\nIYTQoqIAhBBCi4oCEEIILeo/G+1ClQUlG0kAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1a1b521668>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "x = np.linspace(0, 30, 105)\n",
    "y = 2 * np.sin(x)\n",
    "\n",
    "l1, = plt.plot(x[:85], y[:85], 'y', label = 'training samples')\n",
    "l2, = plt.plot(x[85:], y[85:105], 'c--', label = 'test samples')\n",
    "plt.legend(handles = [l1, l2], loc = 'upper left')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<a id='Session2'></a>\n",
    "## Real-world training data may be noisier"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 261,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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Mo9QEg+F9REScIVqJAWfhldbly70SsgtRKrHLaMTy8HBvzBMNknfsDurqHsbQ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\nzcwq5n/5O5xiu229gAAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1a1b4ffba8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "train_y = y.copy()\n",
    "\n",
    "noise_factor = 0.5\n",
    "train_y += np.random.randn(105) * noise_factor\n",
    "\n",
    "l1, = plt.plot(x[:85], train_y[:85], 'yo', label = 'training samples')\n",
    "plt.plot(x[:85], y[:85], 'y:')\n",
    "l2, = plt.plot(x[85:], train_y[85:], 'co', label = 'test samples')\n",
    "plt.plot(x[85:], y[85:], 'c:')\n",
    "plt.legend(handles = [l1, l2], loc = 'upper left')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Create function for generating training samples"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 262,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "input_seq_len = 15\n",
    "output_seq_len = 20\n",
    "\n",
    "x = np.linspace(0, 30, 105)\n",
    "train_data_x = x[:85]\n",
    "\n",
    "def true_signal(x):\n",
    "    y = 2 * np.sin(x)\n",
    "    return y\n",
    "\n",
    "def noise_func(x, noise_factor = 1):\n",
    "    return np.random.randn(len(x)) * noise_factor\n",
    "\n",
    "def generate_y_values(x):\n",
    "    return true_signal(x) + noise_func(x)\n",
    "\n",
    "def generate_train_samples(x = train_data_x, batch_size = 10, input_seq_len = input_seq_len, output_seq_len = output_seq_len):\n",
    "\n",
    "    total_start_points = len(x) - input_seq_len - output_seq_len\n",
    "    start_x_idx = np.random.choice(range(total_start_points), batch_size)\n",
    "    \n",
    "    input_seq_x = [x[i:(i+input_seq_len)] for i in start_x_idx]\n",
    "    output_seq_x = [x[(i+input_seq_len):(i+input_seq_len+output_seq_len)] for i in start_x_idx]\n",
    "    \n",
    "    input_seq_y = [generate_y_values(x) for x in input_seq_x]\n",
    "    output_seq_y = [generate_y_values(x) for x in output_seq_x]\n",
    "    \n",
    "    #batch_x = np.array([[true_signal()]])\n",
    "    return np.array(input_seq_y), np.array(output_seq_y)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 263,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "input_seq, output_seq = generate_train_samples(batch_size=10)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 264,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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aGvTs2TPRoVAkPJ6EJvLWLJPYMzMzUVVVhajryBA5RM+ePZGZmZnoMMiGLJPY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\nQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1c28dfd5c0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "l1, = plt.plot(range(15), input_seq[1], 'go', label = 'input sequence for one sample')\n",
    "l2, = plt.plot(range(15, 35), output_seq[1], 'ro', label = 'output sequence for one sample')\n",
    "plt.legend(handles = [l1, l2], loc = 'lower left')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 265,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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CHnQd2jlOY+RmXWeRLKW4M59zS5gf18oSnVKWH3COECOvNw3XyhKTEleq6rPG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\nZswvDGsdqLzdIEPBCmFA7agXf+HEerfbtB76W1h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ZDEPhM4chSRTR01Z9KY4l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\nAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1c327cb278>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "results = []\n",
    "for i in range(100):\n",
    "    temp = generate_y_values(x)\n",
    "    results.append(temp)\n",
    "results = np.array(results)\n",
    "\n",
    "for i in range(100):\n",
    "    l1, = plt.plot(results[i].reshape(105, -1), 'co', lw = 0.1, alpha = 0.05, label = 'noisy training data')\n",
    "\n",
    "l2, = plt.plot(true_signal(x), 'm', label = 'hidden true signal')\n",
    "plt.legend(handles = [l1, l2], loc = 'lower left')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## basic_rnn_seq2seq"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 266,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "from build_model_basic import * \n",
    "\n",
    "## Parameters\n",
    "learning_rate = 0.01\n",
    "lambda_l2_reg = 0.003  \n",
    "\n",
    "## Network Parameters\n",
    "# length of input signals\n",
    "input_seq_len = 15 \n",
    "# length of output signals\n",
    "output_seq_len = 20 \n",
    "# size of LSTM Cell\n",
    "hidden_dim = 64 \n",
    "# num of input signals\n",
    "input_dim = 1\n",
    "# num of output signals\n",
    "output_dim = 1\n",
    "# num of stacked lstm layers \n",
    "num_stacked_layers = 2 \n",
    "# gradient clipping - to avoid gradient exploding\n",
    "GRADIENT_CLIPPING = 2.5 "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Training process"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 269,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "57.3053\n",
      "32.0934\n",
      "52.935\n",
      "37.3215\n",
      "37.121\n",
      "36.0812\n",
      "24.0727\n",
      "27.5016\n",
      "27.8621\n",
      "29.2104\n",
      "25.2804\n",
      "26.4493\n",
      "24.8914\n",
      "26.5799\n",
      "24.9871\n",
      "22.0373\n",
      "24.2079\n",
      "23.1084\n",
      "24.7991\n",
      "24.0452\n",
      "25.4788\n",
      "23.0237\n",
      "22.9508\n",
      "25.1181\n",
      "27.6942\n",
      "20.5367\n",
      "21.2899\n",
      "28.4336\n",
      "21.9943\n",
      "21.8568\n",
      "26.5138\n",
      "22.5602\n",
      "21.1466\n",
      "22.0203\n",
      "25.0466\n",
      "21.0588\n",
      "23.0585\n",
      "22.5311\n",
      "26.1076\n",
      "21.897\n",
      "20.694\n",
      "21.459\n",
      "21.1082\n",
      "20.9176\n",
      "21.8146\n",
      "21.0299\n",
      "22.3609\n",
      "20.4057\n",
      "21.0788\n",
      "23.2162\n",
      "24.8537\n",
      "22.1202\n",
      "20.7458\n",
      "22.5411\n",
      "21.4423\n",
      "23.8266\n",
      "23.3528\n",
      "22.5934\n",
      "20.2631\n",
      "21.4907\n",
      "19.6011\n",
      "20.5983\n",
      "23.4366\n",
      "25.6377\n",
      "23.4134\n",
      "20.6773\n",
      "18.802\n",
      "25.341\n",
      "22.935\n",
      "21.8413\n",
      "22.1599\n",
      "23.4422\n",
      "24.0427\n",
      "22.8963\n",
      "22.336\n",
      "20.397\n",
      "22.0162\n",
      "21.2389\n",
      "20.5336\n",
      "21.0605\n",
      "22.8863\n",
      "22.3839\n",
      "22.1059\n",
      "22.0032\n",
      "20.505\n",
      "23.4216\n",
      "26.9626\n",
      "22.8875\n",
      "21.9535\n",
      "22.4898\n",
      "20.1734\n",
      "19.936\n",
      "19.7218\n",
      "22.7191\n",
      "20.2067\n",
      "19.4964\n",
      "24.0207\n",
      "21.0039\n",
      "22.38\n",
      "20.1875\n",
      "Checkpoint saved at:  ./univariate_ts_model0\n"
     ]
    }
   ],
   "source": [
    "total_iteractions = 100\n",
    "batch_size = 16\n",
    "KEEP_RATE = 0.5\n",
    "train_losses = []\n",
    "val_losses = []\n",
    "\n",
    "x = np.linspace(0, 30, 105)\n",
    "train_data_x = x[:85]\n",
    "\n",
    "rnn_model = build_graph(feed_previous=False)\n",
    "\n",
    "saver = tf.train.Saver()\n",
    "\n",
    "init = tf.global_variables_initializer()\n",
    "with tf.Session() as sess:\n",
    "\n",
    "    sess.run(init)\n",
    "    \n",
    "    for i in range(total_iteractions):\n",
    "        batch_input, batch_output = generate_train_samples(batch_size=batch_size)\n",
    "        \n",
    "        feed_dict = {rnn_model['enc_inp'][t]: batch_input[:,t].reshape(-1,input_dim) for t in range(input_seq_len)}\n",
    "        feed_dict.update({rnn_model['target_seq'][t]: batch_output[:,t].reshape(-1,output_dim) for t in range(output_seq_len)})\n",
    "        _, loss_t = sess.run([rnn_model['train_op'], rnn_model['loss']], feed_dict)\n",
    "        print(loss_t)\n",
    "        \n",
    "    temp_saver = rnn_model['saver']()\n",
    "    save_path = temp_saver.save(sess, os.path.join('./', 'univariate_ts_model0'))\n",
    "        \n",
    "print(\"Checkpoint saved at: \", save_path)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Inference"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 271,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "INFO:tensorflow:Restoring parameters from ./univariate_ts_model0\n"
     ]
    }
   ],
   "source": [
    "test_seq_input = true_signal(train_data_x[-15:])\n",
    "\n",
    "rnn_model = build_graph(feed_previous=True)\n",
    "\n",
    "init = tf.global_variables_initializer()\n",
    "with tf.Session() as sess:\n",
    "\n",
    "    sess.run(init)\n",
    "    \n",
    "    saver = rnn_model['saver']().restore(sess, os.path.join('./', 'univariate_ts_model0'))\n",
    "    \n",
    "    feed_dict = {rnn_model['enc_inp'][t]: test_seq_input[t].reshape(1,1) for t in range(input_seq_len)}\n",
    "    feed_dict.update({rnn_model['target_seq'][t]: np.zeros([1, output_dim]) for t in range(output_seq_len)})\n",
    "    final_preds = sess.run(rnn_model['reshaped_outputs'], feed_dict)\n",
    "    \n",
    "    final_preds = np.concatenate(final_preds, axis = 1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Plot the last 20 predictions"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 272,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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wQ8JizffrZrGq72kWlDop+ghbVYGfqZikb8wcLQL12l9QqSwwTyy7qKld1PHT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\n4ODgYDMcYXdwcHCwGf8/2a0fIQ3eL6EAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1c27907588>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "l1, = plt.plot(range(85), true_signal(train_data_x[:85]), label = 'Training truth')\n",
    "l2, = plt.plot(range(85, 105), y[85:], 'yo', label = 'Test truth')\n",
    "l3, = plt.plot(range(85, 105), final_preds.reshape(-1), 'ro', label = 'Test predictions')\n",
    "plt.legend(handles = [l1, l2, l3], loc = 'lower left')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "<a id='session2'></a>\n",
    "# Multivariate time series: \n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Input sequences"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 273,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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izy1Z4l2Y+OrMg86kuaKZH2/6cUoOvo7pUhu7umCeaxyXV5MTXi/VDFtv6fh8\ndNsUi7XGk6xyxWFXUFFawQ9f/GHKpCsdjY3qQchW36e7GxpDe5RH7XBQ5wliE3HrLB0D4T9era7l\nlEWnJL6++vCrCUVD/Oa132QofMidiz88rEIcTfG9ivDr6nARwm6X1gVtOzpUwH/xYrbOB4e0cXDt\nwYBa2u6qw67ixe4X2da/LcPSgdyZOvp1tUT3JAkfdY8sy8XXCb+pibZKWGxLFvaZ75nPBSsu4Jeb\nf8lIcCSh8HXoAdC8FLJm6VhJ+IGJCc767GdZc9pprDnsCP7y0F/wSmeiPHK5s5z/+/3/cfSao9mw\nYQNf/erVfOMbnwZUDfsbbvgMV1xxHCtWmJdHPuWUVTy78QFVOcflAiEoEZGUF1x9fT2Ha5MSvF4v\nhx56KN3TzGeYKQ6I8sg63G6lcnIpfLstTlO8K0H4vnA/QYSedlsYIhFFmrW1vFUL9MJSkp3ebrPz\nuWM+x+f/8nn+MrQDODSlRplO+LkUfnPZYDJR3OOhJj7I8PASLCnCpA91fD66OkcpiUJtOHlTvKVe\nrlh7BT/5+084x/4joCbD0tHbuWBB6qGlhK4uyTnBNxKzX+2VXhbEx+jpMa26MXMYfI7HvQMsGbXR\nUpm8wYfVH8a6hnX84pVfcMHIpwGRQfh//GOyAqgRifhJeE+C8AXgdUWYmLCoRHJHh2qEzcbrjU4O\niXkpsSePfdmay/jiY1/ktpdvY2LiRymECSq91zCxMwUpk64qjoFDD00QvqUKf9484o0NtFfCWeHU\nKeNffM8X+e3W33LTMz9lYODfMtrvdCpi/+yjn2XLvtR0tXBYpTV6mYCtHojFmArGiVCCJ4+FdNYu\nWMst/5SjPPKf/0xDbS3/+8c/Muy28VrHa5TIZCfo6enhth/cxq8e+RUrm1bzTxs+wNq1axLf9/X1\ncvvtzxIK7eSKKzLLI7/wwiAXXng0nznpfoQ2nCkhTCDLiKa9vZ3Nmzdz9NFHT39xM8ABpfBBKeZs\ni4K0t0NT9aTKwff5YMkSKkgGwQqGLrVra9njUb/kkrRO/4l1n6DeU8+9r6jgp9FSqKhQL61shL93\nLzSV9CcJ3+ulmiGGhywaoRgVfmSIxgkQabNhrj36WmLxGL97URXFSbd0wHyEMjoKwaCgke5kpK6y\nkvqSIcstnWg8ylPOHk55S2ZE0a4+/Gq29m9lx97exIQfHc3NilTMSjol8sb9OxKED+Bxhq2zdDo7\nE1VKt86TrJpMlfC15bV8ePWH+a+X/ovhsXCKpQPqXdHVZW6ppUy68vnA48HnU4RmGeEPD0NNDfvc\nkpATFk2kzihaPX815x1yHj/7c7NjAAAgAElEQVT6ywOJ9hqRK5c9HgchtN9SexsLJBJrgs6rDj2U\nx/7+d754441sfGYjngoPzniS8Ddt2sRJG05iXu08RkLjnHLKBaoev4bzzns/druNxYvNyyNffvmp\n9Pf30GcYDjplmGg08/fy+/2cf/753HLLLVSk/8gF4oBS+KA6Ubal89rbobVqDAZJKnz+ACjC18pn\nzB46U9TWskeoBXaXjKfe4jJnGTeccAPX/lmxunFWpxC5A59dXXBCWW8a4Q+zfdB6wu8KDdA4Tsb0\nx8VVizn34HN57O5XgQtSLJ1cllRKSmn5ysR5Gvb109mbo/jRTOD3Q1UVXeNdjIspjuxCMbjmmQJc\nvPJirv/r9Ty2/SUqK8/BODIypmYaX2SQfAk3jb4OdReoziIEXkeQiYksU3Nnio4OWLuW8alxOjxR\nPr43s0jMd0/5LvfvuJ99Q5N4PM6U9jc3K8Ls61MVJdMP7bBL6mO9iReuzx2FMes9/LZx5R8tHszM\nmfzKiV/hgUeuAzIXvikpUW0xU+JvvAHhQJgV8ddVLQa/n4Gdg3TQyurVSQ99tli2eDEv//rXPPLW\nW3zr69/iiPcczq2fTi62q6fzziufR7cWNDMSvstVasjUySyPvHWrk/edvZCQYehYIlW1tUgkWQ8o\nEolw/vnnc+mll/KBD3ygsIsywQGn8HUf1kzltLdDq1eLcFZWQnOztQpfj2TW1rJHDlE9CZUDmQbv\n1YdfTYVoABGjtDSVrJuazBV+IKDStJvoTiH8GoYYHraoNMTYmHrreL10B/toGsc0heNzx3yOwGg5\nwh7F50u2v65OBbLM2p/IwadbZdIAVFaqejpWZul4vfQHVBBhgZ+MiKq31Msd597BwHCEkCN1AkCu\nyVd794LdLlkQ7lCBC4cDamrw2ALWKPxgUAU/Fi7k9X5VhWTVQObjOd8zn2+d9C0iky56w6n5oLnm\nEnR0QHNdSKWU6oTvUYRsCeFHIuohqq6mbVQFqBZ1Zfadw+oPY12NiqsIV+qJ9Vx2M8UeiUCJLZpk\nWc3DB2tm2/Z0danyyJdcwpWfupLdW3chDCSil0e2T9mJR2w88cT9IFIbmp6Lr5dHttmcbNr0JF29\ne1PeEk6N8HUfX0rJlVdeyaGHHsrnP//5wi/KBAcc4be0mA/LEzn4ZX3ql3G5oKwMn0b4lnR6A+G/\nGexmyQims4pKHaUcVXcylPj59J8/lVKyINvkJZ0wm+MdGQp/3G+zJp93bAy8XqQQdPl7aJzAtMDJ\n+tb1rPGejizv4/rH/jWhaGw2pSzNFL5+TY10J8uBVlZSH+tmYMCifGTN0tFnRc73Yzr19Pzl59NU\nsooh+Sb3b08ubKxnjZgR5t690FAXVYSpy/+6Orxywpqgrf6WaWlha5+qoLeqy/ymXLX2nyHm4sne\nB+mdSEa8cxF+WxssqtXeTJpNUFmh+p0lfV9Pe6qpoW1EEX7rHvNsgvcvuRSATz/2sZTZz7kyXcJh\nKBHRZDqPlqUD1hD+1tdf56jLL2ftscfy05t/yievvSpFNerlkY8/7nj+5SMfZ/Hi5dhckrhhm/TZ\ntnp55COPXMejj97NQa1LUglfm22rt/+5557jrrvu4oknnmDt2rWsXbuWRyytX32AWjqgFM38+cnP\nVQ4+tDq7lbrXhlYVZREIWqzw581jz8hbHB10ZZ1V1FK2Ao9nnFtfupVYPMatZ9+KTdhoalJpiulF\nlRI5+NF28Gi+nsdDDeqhGhnJtCFmjLExqKhgODjMVGyKJr8ta5L2QscRdNV2c/PzN9NU0cRnj1HL\nhmWzpPTPGuhJKnyfj4ZwO6Dei8Y0vVlBJ/yARvgBstYaqLUtxV/ZzxUPXcG6hnW0VLZQU6OSZMxi\nQF1d0FwbhF5SCb9vlEErCD/heTWxtf9+KuJOFnabHzgYUI/tlH2QM35zBk9f/jRVZVXTEv7ZB2vp\nOJrCL69wYCfK2JgFNKDHr2pqaBt9hfq4G9de875f62gFYPfEK5z661P562V/BZLxlHA41aKJxxUp\nOh0REHOj8M9Yv54z7rkHVq9m68gu3KEYTMVNyyP39ET50IfO4+gzTqJ9rJ0777wTUM9oOAwTE6nl\nkcfH1RyOg9mJt1Hde39nJ6G2nsT1ARx//PEZK2tZjQNG4XePdxOKhhJZL+mdPpGSKTpScvF8btVb\nrFT4kcoKOsc6WRLzZa0bEAgI6qsr+H8n/D9+/srP+fGLPwYUYcZimamNCQ859GaGwgeLyiuMjyv/\nflydrDHsylrCcGBAcNjSRs486Ey+9tTXGAkqhZdrhFJXOUUJkRRLpy7YoR2vwLZLmbB0dIVfFyBr\nkvzYqI0Nh6xFSsllD1xGLB5DCBX0N64zrGPvXmj2aarAQPie8Ig1lo7+YqqoYGv/VlbKOsSIeYlk\nXZxce8Ll7BraxVm/PYtAOKDHYjMsqclJ5esvqtAEiUb4wuPGZ7eotIhO+NXVvDXyFosd89Q1mSgp\nXUPcc/HtbB/YznV/UZ5+NoWfmHQlImmWjrKkLEnN1FhX2u1E4hGc0pZR2Ecvj3ziiStpbFzExRde\nyHBwmEA4kGi/lJn1gFJSSg3tt6HOaWl5iGlwQBD+0+1P0/SDJp5ufzpF4RuRIPzYnmSWCFDhVnfb\nEoU/MAA+Hx2TPcRkjCXOuqwKX4lRwY0n3chRjUfx36/+N5B98lXCEpl8Y+4If2xMZehMKLXZFC3P\nqvD7+2F+neA7J3+H8alxfvTij9Q+Wgwinae6u6GxSqv4aFD47ri68QXP9gyH1ZPv8dAf6KfC4cYV\nJavCHxmB5vkefnLmT9jYuZHvP/d9QM1YTc9lVyml0FSm3WSjwp8atMbS0W+A283uod0c6qxX1xQM\nZmyqn++YJcu55/x7eL7reX7+8s8RwnwuQaIMd5lWAKwiOUL0iXFr8vD1DlhTQ9toG4vcWkc26f/6\nC/J9q07lo2s+yh+2/4G4jKcofCMSk65kODnsFQK7sJDwNdaNCanagi0jEHjTTTexZcsWHn98J1/6\n0o+o99bjsDnoGu9CSpm1/RmzhAEcDuzaC8uqZRrzwQFB+Ec0HIFd2Hmm4xkqK1Uqtlmnt9uhaWpP\nqsKvUMxkmcKvrWXPsJoIsNTdnFXh63OEhBBctOIiNu/bzO6h3Vlz8Ts6oLZWUhYPZARtwaJ6Ojrh\njyvCb4y7syp8vY7OmgVreP8h7+eWF29hLDRGY6PirvQXaFcXNPq0J92g8N0ooitYJesH0Cyd+aU1\nqZ8bEI+rS62shMtWX8aFKy7kq099lbaRNpYuzSzANzSklm5sdmq/pZ6aVFeHJzyE32/BMFwjfFle\nzuDkIPPLatXnJmysE77XCx849AMcXHMwf31L2SJmhJ+Y5OfsUukgekqIx4OPMUsVfqSqgq7xLhaV\na4Rv0n8CgeQyhR9Z8xEmI5NMRiZxOJTTmq7wkwo5nOKB2+w27CJuHeHb7URi6uQlwpGVifVZtnab\nnXpPPRPhCcanxrOOUMJhlSFlQ5oq/CLhzxCeEg/rGtbxdMfTOVVOczM4xodTCN/lceAQUes8/Npa\n9owowl9SrdWsNRmzGRfauHDFhQgE975+b9bUxl274ODFWs+eY4XfNd6FQFBv85lK72BQtV8Xul85\n8SuMhkb58aYfZ83F7+6GxgrtJutBW58vUZ6gYIWvE7vXqwjfrTXORH5PTChCV6EcwdfWf41oPMrG\nzo0sWaI4yvieTuTgs1epY50w6+rwMkEwKAonHa394yWSaDxKjVt7qZgsZ6b3VX2m7SmLTuGZjmcI\nx8I0N2daOgmFb+9MGd3iduOLW1QTXyP8TsckcRlnkUcLyJgQvrHvH9d8HIurFhMIBxDCvMxwQuHH\np1JzIe12HCJmLeHHFVs7sU9L+ADz3PMosZfQPdGNs0SmtNfYfqdDEwUGwheouQVFwp8FTmw5kU3d\nm5iMTNLSYm7ptLaiFJOh0wuvxzof06Dwyxxl1Fe3qI5kQjoBg1BvrGjkhJYTuOf1e6ipUUPDdIW/\ncycc0qqtEG6YaTtXls58z3ycZeYKX/fbdcI/vP5wzl52Nj944QfUN6inz0j4U1Pq1jS5NbVqovAL\nJnz9HmuWTp1Hi9ibKHxdNOuT3g6uOZgyRxmbezebVp1MxE+i7amRcY3ws5xmZtBuwKBQ97u2Qpuq\nbEL4BrsfgJMXnUwgEmBT9yYWLlSjL6MT1NamktLmh/emFuDxePDFh60pLTI8DA4HbVHVORZXtqrP\nsyh8vQsLIfjI6o8QioYIR8OmZYZDIRXQtctoaibDHBB+OKbY2mmbXuED2ISNek89k5FJYqibbmbp\nlDi0YxkIH8Au4kUPfzZY37KeSDzCi10vZh3WJgjfOJ/e7aZC+C1X+IurFiN0YjPxYf3+1MXKP7Ti\nQ+wY3MH2wdczAp/Dw+ohPqQ5aVsAquqeYxK7iFln6VSoIXlTRZNqoMkDqycjGSeqnX/o+QwHh5EV\nquHGF66eZ9+oe+BzQfhGS8ffx3yfNtQwednqHKp3A7vNzpoFa9i8b3Oi6qSxPEdC4U/uyiB8ywqo\n+f3gdDIUVe2tqWxIbawBRksH4KRFJyEQPP7W44kYlrH/6H1fjI+lKnzd0hm1gPCHhlTAVs/Br9SK\nRGVR+Ma+f9may9QhgkOmCj8YVNlTiWqWOmw2HMKiejpplo7T5lSfmQTN0wunuUvUxYRiIVyuzMdd\nKfw0wrfZVAHEosKfHY5feDwCwdMdT9PSovqfTiJTU4p0Wpuj6tcwEr7Hg09Y5GNqlTLbR9tZVLVI\n66VkJXzjLNsPLv8gNmHj3m33Zky+Siytt2As0WYdosJLVelk4Qp/akr9pyn8Rm+jImYTJtY/MrZ/\nWc0y9V35dtxueC25OFMy4Fw6qJSNHt3y+Swn/Ii7jKHgEPMr6tVTmUPhG7vBYQsOY/O+zTQvjGO3\nZyp8hwPqRnenVoubNy+h8AsO3AYC4HYnqjHW1mqWSB6WTnVZNYfVH8YT7U+YpmYm1l0YG8u0dKz0\n8KuraRtpw2lz0ljdqj6fRuGDmr1d6ihlKDiUqKej86yUSuG7XFIp7jRLx25VATWDpWMXduw2pcCv\nuuqqlIqVUmYSfqldWXyhaIiystTHXU8pLbGnEr7H6034+Drhh0IhjjrqKNasWcOKFSv42te+ZsGF\npeKAIXyfy8faBWt5puOZjE6fyMGfp3W+tE5fIccKV/iBgPqla2sZnBykrrwuqWTzIPw6dx0bWjfw\n0K6HMhYSSSytN0+T8cYdvV6qS/yFE76xcNo0Ct+QUJKATvhvjuxmzZrUpRoTKeaOfeqe6NPLKysp\nZzLlmLOGxrgDTiUP69zz1X0yYeJ0SweULTU+NU6Xv42WlkyF39gIdn8aYVZUWKfw0wi/pnZhamMN\nSFf4oHz85/c+T838yUSbdSQIX0u7TcDjoZJRxidE4fVotDo6baNtLPQtxO7RGpfH6BbA5XARioZw\nOuMpqY3hsCLNMn1GerqlIy0ifO1lEo6FVcE6jZhvv+02li9fnrKZlKmEb7fZKbGXJAh/airZ/sTC\nJ3btA+MLy+FIsXRKS0t54oknePXVV9myZQuPPvooL7zwggUXl8QBQ/igbJ3nu56nvlE99LqtkEjJ\nrNZILU3hV8QsCFwZZtmOhEaoKqtKKvw00gyHVUcw8jbA6rrVvDXyFo2NMiW1cedOFcxq9Qwm2pyA\n10uNY6xwS0e7AQGvi9HQaE6Fr1+O8aGtKauhylXF7qHdibV5deXy2mvqAWl1dqXu5PNhQ1LmjFim\n8PvtKs4x3zNfMWIelg4ohQ8kbB2jwk/Ubp+cTP6mAG63dQpfUwBDk+qHrF2wOLWxBkxMKE/eWPjt\nlEWnEIlHaI+rFb10sTM6qv5LKPx0D58x4nFR+AtLq6PTF+ij3lufFDt5KHwAh00xqHAo9tZtHf19\nUVaaZolofztkJFHKvhAE/H7Ouvpqzj7hbM5bfx73PvQQABtOOYWXXnoJgDvuuINDDlnGxz++gX/9\n16v59KeT5ZFv+spNnH/6+Rx33GIef/w+LbHBzxlnnMKHP3w4G844igeffjpjhGKTSYUvhMCj3ZhI\nJEIkEkGkl20tEAfUTNsTW07klhdvYbh0C3BUotMnCL/CUEdHh9uNLz7M9nFJQSWGNYkd8rmZ7Jqk\nuqwaHOYK359mxetoqWwhEAlQPX+SUMitiyZ27lTr3TqCE5k7ejxU20bpLVTha4TfXaYkiVL4+3Iq\nfP2ZBtVZl9UsY/fQbi46DH72M5XeuHQpbNwI69ZBeXgsdSeXC0pKcNunCAQKrE2t3dQ+m2rvfF3h\n52nprKxbicPm4JXeV1i69IP87nfJ77q64MgjgVeDqYRfXj4nlo5d2PGVVytyzmLppNfCP37h8Tht\nTjb2PMaCBacn+n7KugtZLB1Q9yT9mDPC0BAcfjgjwQ5VkjqL2AFzhe+wOYgRA1uYm28uYe9eJRL0\nssgetw0ROFh702k7TS0gEoYQeopz9uatXQu3ZK+OzKMbN9Iwfz7fvecWvCVeqke1a9JUV09PDzfe\neCN/+9srdHZ6+dznTuaII5LlkYf6h/jFH3+Bvb+Mc899H1dc8UGqqlzcfvsDjI5WUO/axfr3nsq5\n116bZBm7HRsxIoaXVSwW44gjjuDNN9/kU5/6VLE8ci6c0HICANuDj2O3pyp8ux0aS7T0krRhbQXj\nhQeuNBYccanjVJdVZ+30Zh44wEKfGsaXVKlptvpCLjt3qkWiTN8UXi/VjBRu6eiEX6IKOjVWzEzh\nAwnCP0yJZbZsUf7rpk1w/PHajqlvCRW4tU9ZZun0xdW/uRT+6Kg6tVHsljpKWTFvRULhj4yod7g+\n6aq5GfXiNrbfbsdTol6QVlk6Q8EhasprlLKrqsqq8NOr5rpL3BzZeCR/2/u3lNTMREpmS1ztaBK0\nBQvmoWjqZDg4nLPvQ6adCQaFXxJCiKQlosoiq1LIagPDTkKA9nlBllQ8zqrFi3nsuee4+Zs3s/nF\nzfh0NaAdeNOmTaxfv57KymocDifve98FKYc469yzQMDyVQcxPNxHMKiKoX3jGzdwySWrOeui8+ke\nGKDPOKXc4cAmYymjE7vdzpYtW+jq6mLTpk28/vrrBVxYJixR+EKIXwJnA/1SypXaZ9XAvUAr0A5c\nKKXM7L0Wora8loOqD2LLwEs0NZGi8JubwTFhMpZ3u/EZfMxZj6A0xhp2qiGpUvjmQVudHNIJUyf8\nuuU7sdkW8dBDanGoPXvgggvISvg18QHLLJ0umyLIhIcfiZC+OoyZwgdF+He9dheLlk1it5ezebMq\nphYOa4T/+mTmTj4f7lDQGktHCPojSr7XuesU4Zsw8ciI4j1bmtw5rP4wHnnjEa5ZokZ7e/ao7Jap\nKWhuiKnom1HhA153HMIWWTrz5jE4OUhNmZb+lIPwzdT44qrFPNv5LEcshG3b1GcJhT/Pr8jLxNKB\nAgk/GFT/1dQoO9NVpW6uWcoKiXdbCuzCjkAQiU/xjW8oobBqFWzfrpT+soYg7Nylhrr6S2vfCCNd\nfvawlOXLM7tW3ojHWdbSwgt/+TO3/fV+vvfN7/H6SS/z1fPOS2yi17hJ2i+ph/CUqWdyKhZCSkkw\nCL/5zd309Q3wyCMvs7R8gNZ16wgZU5DsduwyZpqWWVlZyYYNG3j00UdZuXLlLC8sE1Yp/DuBf0r7\n7EvA41LKg4DHtf+fczT7mumd6GXhwlSF39pKslene/iME4kIQqECTqwrfM2DrHJVZQ3aZrV0fKoQ\n0JjjDU45BX73O+Ulx2JpCt/Ys71eKmNqen9B+bxa0LZbsygSHj5kHaGkP7QHVR8EQNfkmyxfrtYl\n2LhRffee95Cp8EEpfBGwhvDdbvoC/bgcLrwl3pxBW2MX0HHYgsPoD/Tja1AqbM+eZPC5uU6NfNIJ\n3+OWidMXBIPCry3XZtlWVuZt6QA0eBromeihuVnS2an4va1N8WOVLbnWQQIGS6cgwtf6TsTrxh/2\nK7ED6rdO6ztSmit8IQQl9hKmYlP4fOolGwrpGTokmTbdA7ditmosRs/AAE53GWeefybX/su1vPLq\nq8kGkyyPPDQ0QjQa5eGH7085hL4yWSiqRijBIAwMjFFVVUd1tZMnn32Wjt7e1DeF3Y5NRonH1TkG\nBgYY1fzGYDDIY489xiGHHFLAhWXCEoUvpXxGCNGa9vH7gA3a3/8NPAV80Yrz5UK9p57n9j7H8S1J\nsmlvh9NOI2neZun04+MZz3P+0BW+TRFDdVk1xMyHtdkIv7a8FpfDRedYJx/6EFx1Ffz2t+q7Qw4B\ntvjVQ2TMVPB6cYf1TpJ5zLyhK/zoMJWuSpVbrDP65GTKPZucVEFkR1rv0TN13hh6g7VrV/PYY+r5\nPPRQqK1F3aP0tQ99PtzSb42lk5hlO19ZIlkU/uhoaoaODj1wO+J6GXgvb7wBN98MDQ1w2jHaiyOt\ng7g9InH6gpDw8HcmXpxUVamVP9IwMZG5wAlAg7eBcCxMzYJJJifd7NplmH9iyMJKwCqFr4udcgFD\nmtgBda/S+v7UlCLndLEAijTDsXCiiQMDWoaOnoMPGVk6VhH+1jff5PNf+DwRYnjLvNx2yw9TNtHL\nI59yytH4fA0cfvhyfIZ7aRd27MJOKKpUYzQKp512Kb/5zTmcdto6DjtoKYe0tqae1+FIScvs7e3l\nox/9KLFYjHg8zoUXXsjZZ59dwIVlYi6DtvOllL0AUspeIYRp8V4hxDXANQAL09c8mwXqPfX0TvTS\n0iL5zW8EZ56p5eC3kjRvjfJIU/igOr2xpPKMoBO+UGq+uqwa4jNT+EIIFvoW0jnWyQ3nwT//M/xI\n1STj4IMxl0YeD+VTSgVOThZO+APRMWWHQFKNp7FxIGA+fD6oRhGV7uPfdRc88QR8+MPaBtkUfnyC\nXisUvlZHJ9H+LAp/ZMRc4a9dsBaA7aMv0dDwXn76U1UZ49e/BrctrfCbBpvXjcc+id8/Wz8htf1D\nk0Mc03iM+iyHpbNsWeYhGrxqstaaE7qoqjqYE09UL9xjjyXJ6HNh6WgdeljLpKkq0wjfROFn6/sA\nJY4SxkPjlJYqVa/b3WVlwJR5lo5VhH/Gscfy1CXvo2Oqn9XzV1MSicPrr/PUgw8mZhhecsklnH/+\nNbzxRpQbbzyPM888HSBRHnnHwA6CkSC9vX527wYpa/nd755n+XKU6hwb04hIZfAwMICdMFIK4nFY\nvXo1m7Mt12cR9nvQVkr5cynlOinlunnGSS2zRL23nqnYFJddNcYXvgA7dqhR2apVJLMUjJ0mTeHP\nGjrhS9XBZxO0BWXrdI51Ul0NZ5yhHu7GRu0dZUb4Xi/lWqAyS52z/DCmMmhGw+NJhWZU+AZMTpor\nNE+JhwZvA7uHk4HbYBBOOMGwoxnhR8etsXS0sgrz9bIKORS+GeF7S700ehtpG21jyRJF9uvWwaWX\nkrwH6UNAtxuPLWiJwpduVTgtYelkIfyslo5G+CV17Tz/vOL2vj5Dhg6kKvzycmsVvlOp8BRLJ03s\nZLMDQU1gisQjxGWcysokib8dlg5ARDuW0+ZMnsfgk379619n/fq1XHTRSlpbF/H+978/5TD6XAK9\ni8Tjhvdr+qSxRPvf3oqZc0n4fUKIegDt3/5ptrcE9R411o25e/iP/1CZLp2d8P73k1FHB8hQ+LOG\n3uljk9iEDW+pN7mWap4KH1TgtmNMBR8uukh9lrDxshG+NnmpYML3+RgJjlDp0thwhgofkpk6a5IZ\naypgqzfQJGjriVhQU95QC3++WyN8j0fd+7SZOdksHVDZPf2B/kRNnVtu0Z7TREJ4JuF7bf7CCD8a\nhakp/O4SIvEINeVa0FZXyGkpKNmCtjrh90z0cPDB8MILcM012gjLjPDtdspdEoctZhHhG+JXxvYb\nkFPhaz640dZxOjXrcI4tHYAoUgWPhUiSs+HAN910E48/voX77tvJD3/4o4wceZfDRSQewWaPJXIc\nchK+ZukU3P4ZYC4J/yHgo9rfHwUenMNzJVDvVYSvL/0mhMrQsdkwl3ZWKXy/H0pLGZ4apcpVhU3Y\nsmYqZMvSAUX4+/z7mIpOce65apvVqw07zjHhj4ZGk0PyLArfLMtCx7JqRfhVVWr02tCQGMVmV/ix\nMQKBAtNi/X7iHrcqnKZbOjorpr1Nslk6oLJ7+gP9XHcd3HmnFmyG5G+Y3n63Gy/+wl5YeuG0cnUP\nEgpff7lMTSU2jcXUbUxPy4Rk3++ZUMWLamvhttvUmt+mHj5a8cCSYGE18c3iV2BK+LkUfoktSfhu\nt+L2xPvVTOFbZeloO8eIJ0oqJF4saQc2a4YOl0MJPF3lC2F4XLMq/JktglLoilhWpWXegwrQ1goh\nuoCvAf8O/F4IcSXQCVyQ/QjWQVc5vX6ThUfSJ56AtQrf7WY4NJzs8GAauMpF+HqmTtd4F0uql/DS\nS4Y4p9+f2X6rCH98HCoqGA21UVmaW+Fns3RAKfzByUGGg8N8/vPqPqh0aWm+o8+HGwuCtn4/I8ua\niMlYUuEbCV9j+FhMXU76bdRR565jx8AOVqyAFSsMX+RQ+J5C17XVCd8VhwDJtExjLSZttGhWVkGH\ny+Giuqw6QfgpMPPwtfb7ggHGxmYb/Em2f0Qowk8IhrKyjDKu2RS+y+UiMBYACVPRKSpKlRWVyAZO\nJOSnZblYqPBjxBPzARLnykL4ZunbRsKfP99NZaWB480I32ab0SIoUkqGhoZw6c7BLGBVls7FWb46\nxYrjzwS6pWNc3DmBQCAzKmulh+92Jyee6DDxMf1+leViXLdTh56L3zHWwZLqJaRkZfn9ySWxdHg8\nlil86atgNDSatHRyKPxsszKNmTrXXmuYJRgKKdI3U/j0EYmI9HT/mWFigr4KpcoSHr7OKgY21n+K\nbC+suvI6+gJ9SClTh+w5PHyvHGOfBQp/qEQ9/BkKPxhMeFC5CB+U4OnxZyF8m8006O8bCVhi6Qxr\n/TDFEszTw29qaqJzb+MztvAAACAASURBVCf9ff1E+iMMugZTNxgaUr/Bjh3Jz6REDvYzyA4iEdNw\nR34YHYWxMfbJCQQCMSiS5wyFUvrP8LB6DPX6VkZIKRkcGyTSF0ncg8T8mN5eNWowMns0SmhwiEGi\n7N6ddIBzweVy0aQvmjELHFClFUAF3txOt7nCT9RZNaC83FqFHxxmXrkh+JxF4WfLptEJv3PMZCXq\nObZ0gs0LiMQjmR6+SdA2PbtSh56p88bwGxzddHTqTsZj6qioSKmYmc1qmRZ+P33arTFV+NM0Q0ed\nu45QNIQ/7FdxGB25FH5srDCFr7VvUCv8lvDwTaqtptfCT0eDt8Fc4WsjuMwZQx58tnFrPPz4JBWl\nFUmVPAMP3+l0smTxEk5+6GTWt6zn1+f9OnWDj34Unn46OXUYlIBYvZojRJBrP+fk+9+fZfs/8xm4\n6y4u+u5CFlct5oEPPaA+P+00OP10+OUvE5t+/OPw4INZF7LjhO+fwEUrLuKnZ/009Yvzz1dDxj/8\nIfnZ0BAvrr6K9/Ii//u/cOaZs2z/DLDfs3TmAvXeevNOb0b4djvOMidljrAlCn8kOJIc0gIZ9VIx\nLx6lo6miCYGYEeFbUmJ4bIyRKiUxMjz8GQRt9RGWvpB4AtmY1uMpvP3abJ7+MuVvpqRlQopCyybU\ndej79gfScgxyefjxMSYmCvBWdYVvU4RvqvA1pJdGTkdWwk8vnKbD7cYnrCH84ehEMmALM/bwAVor\nW2kfbc/8wqwAj5ZiXW4PW2RnGka3eiNN7MxcM3pry2sZDA5mfmG2o9tt3YpveeLAJHxPff4KH5SP\n7wxapvCrXdNbOtk6fKmjlAWeBXSMdmR+OccKf7RCeUz5KPxs7dcV3lAwrdZDNsJ3uwsn/FAI4nH6\nXSpLJFfQNh+FDyaEn8vSYcKaoK0tiE3Ykvc/h8LPSvieBnoneonLNFM427DS48EnC6wWGwiA3c5I\neDzv+FU2wdPia0lkqWWcw2wnr5dye8g6wi9NI/wZJCyAIny94mkKzAi/tBS3Nm+n4Cy1PHFgEr63\n3tzDz0b4bjc+52TBCj/mLmc0NJpXp881QWqhbyGd42kKPxLRygbOAeHH4xAIMOpWHniCcFwupaJM\nFH62Ti+EoKasJlHXPWUnyNzRCsLXWHCkJG3iTw6FP2PCz2bpeDx4tCydWSdQaE/7kFRVVm3CltrI\nGVo6MRljIDCQ+kV64TdD+ytio9aMbkNpo1uTtNJ8FH7XeFdi5akEsj00FRWU2won/FiFl/GpcWsU\nfnrf13dM7ztCZBtEzxkOTMKfqcJ3u6mwFR64GqsoQSLzCtrmIvyWypZMSyfbbC0rgrbajqMu5e8m\nOr0QGcNyKXNbOqA86LdV4WuEOeaI4na6kx6ylQo/Vx4+E0gpZn//dYUfm0hm6BjPNUNLB8i0dQyZ\nPilwuymPjpvVOMsfuRIWICWtVFvJ0TRhARThx2WcrvG0RZ2zqQyvl3KCBY9ux6tUW1MI36Ra7LR9\n30zsSJn1hauX5igSfgGo99TjD/vxhw3jpFhMlW3MYun4bBMFq5wRj1LIGR7+TBV+hSqvkJJzm20s\nXFqK0ylw2GKz7/TasUdKVZZIrk4fiahbmWtYW1NWkzmsfTsI3x7F5zLkW+qsOAOFP8+tAu6mhJ+Y\nBWSAwYeddeBWV/ixiaR/D7OzdHIRfpa+Xx4ZS1mlacYwKvx0Dx9S+v90loielpzh42d7aLQRbqEK\nf7RSLVOYj8KfztIZnBxMfXb1ZbtMOl2Z24YgXiT8QpDIxTfaOnopzCwK30vhhD/sVrczw9KZocJf\n6FtIKBpiYHIgdSfI3ukdBQSutN426tQsEeNDm+ZjZiuNbERteW3+Ct+KoK3GgmMijK80tXSA8ftc\nzdDhcrioKK0w9/Bz9J2008wMusIPj+ZN+LksHZgp4SeL780KgQDSoxR+St8xKS0yXd/X298XSAv6\n51L40l8Y4U9MMOpV+cBWWDpTsSkCkUDqTmC6o/C4cdtDRQ+/ECRm2xptnWxDclCdPu4veFg7XK6G\nZxnDWpPAT65O3+xTC1jvHTMsTDod4dunCid8rbRzikpOU/jZFj8xwnRYm63Tl5VZp/AJpbZdzzuf\ngaUD2mzbSROFPw3hz/qh1bN0QiN5WTpOJ5SWmh9qgUfly+ZN+G43ZQTTTzMz+P0EvWWEY2FzS2cG\nCl/ffziYtqJPDoXvjk8UppDN4lcw66AtkDrCzZUa5laEX1T4BcB08lUuwne7KSuE8GMxmJpiWLNI\n81H40xEmpHX66Qi/kMCVduxRW5hyZ3mipgmQVeHnbH+5snRShrXZdrTZcGvplAUTvgymKnzIqJiZ\nLbvSCL28QgqyBT0tsnRkeVlq4TTIqvBzLUXotDupc9fNTOEXGgMKBBj2qT6TEbTVz61hOoWv75/S\n9/XAkVmnq6igPDox+7ZrKb0Z8SuYtcIHUgVPrk7nduOxYj2IPHFgEv5sFH50vGCFrHvgGT6mocNn\nWwDCCP2FMRIyTB3MRfgeD+WigMCVrvBFKLXDQ4bCz9fSicQjqTGUHNLaUx5POfaMoTHtaCyQqvAh\no2JmPgp/vnu+OeHPocIPVLqZik0lJ12BqSVitrxhOkxn284x4Y94VWyjUIVfYi/B7VTzWRLQ0m6z\nip3IGJOTs0yR0gr0j2piLSN+ZZJllI9YSyH8XJ3O48EtJouWTiGoclVRai+dkcIviPD1euD6alfp\nQdtIJFGxUa11mZ/KSen00yh8N4HCX1gymPqyggyFn6+lA/l3+nKv3diMmUNX+BH/tAp/uolXkEXh\n5/DwC1b4gQBD1YpxplP42UojG2E6+SrHC8sSwtcskUI9fFAvjeGQyeg2a5ZOAX1fH92WmCQsuN3J\nDBvUOycUmoXCz0X4brc1CwDliQOS8IUQLPAsmJHCLwuPEw7PMlNBn2noCOMp8aRaImkP7XQTTyD5\n0MzI0pEFDAv1Th+ftETh6yo1JXA7Oak8dZN8PLunDJdtavYqJ0H4E5mEb6LwszQjgTp3HYOTg8Ti\nhs6Qw9IpOGjr9zOoZYmkePh2uzLsZ2DpQHKpwwR00srW9wv18HPFr2BGCl8/Rkrfz7WARKFZOomE\nhRgCkVpOI62WVD6jw4SHn973s+3oduMpNAYxAxyQhA/a5Kt8Cd/tplwLHM6q0ydWu5pK7fCQ0enz\nIfwyZxkuhyt/S8frpTxWQKaC3uljgUzCL0DhZwSuysvNywwWGriamCDstBGKhjItHbc7g/CzNUNH\nnbuOuIynks4cWzrDFSpLJKP/pMWA8rV0+vx9ROPaOgDhsCL9ubR0tEMX6uHrxzAd3WZV+JOEwyJ9\n2YP8oIsdewSfy5ec9GY8n9Yx8+n7la5KbMJmrvCzBW3jBc7UngEOXML3pNXT0Tud2eSTQjt9ojxs\nKNMSSVP4ucSKEVWuGXb6eAGBK53wIxN5K/x8MhUyOn02aeR247YFCxqhjNWoBmUo/DTCnC7oBlkm\nX2WzdOx2PKWKaQqxdMY0DzzjhZXW/ukC/qDEjkQm6xlNK3YK6PvxOExOJpc3LDAPH2ao8A3PbiFi\nbVSEzcWOYZt8FL7dZqe6rHpGQVtL1oPIEwcs4Td4G2aWpVPIsFZX+PHJ7Ao/zdLJq9On+5jZaip7\nPJRHCo9BjIbHp1X4s7Z0cj3pbjduJgsjfG2m5HSEOWvCz6bwAYfHhcseLsiSGi/XCH+aF1Y2Z8mI\njCyvXHNQChU7WttGnDHswk5FqWH4MVsP31Wdv51Z6AtruoQFwzb5iB0wSUueztLBT8BfJPyCsMCz\ngJHQSLImx3RZOhZ0muG433xIbjhwPpYOZBnWZutpickns+w0gQDx0hK12lX6CCUtUyGfYW2VqwqB\nMLd0zKBNvirE0hmrVPfZSoWfMvknF9O63XidocIUfpnymKx4Yem2ymhIW8ZquviVFWLHocpqp6wh\nkKbww2GVvzAdYVaVVaXambmYttCJe7rYkUFLFD6Y1NOZLmhLoGjpFAr9xxub0grkzOWwVu/0kYns\nhD+DoC1olo6x009DmIUGrvxVbrV4dLZOn2ZJTTesrSqrygxc5bJ0ZAGBK7+fMa3Spylh6gp3mmbo\nmKnCx+3GYy9gIfNAgHEtD9xbkhaRNVH4uTKMINn38yJ8i/r+iD08bd/P186sLqsmFA0RjGjtni4l\n2QqFHzNJWEgL2ubT98FkpnkuD197YU0GxeyL780ABzzhv10qRwIjkXFLgrZg4mPmetINhD+rTuP3\nM1qljp11WGvIVHA4cme5QJZhbS7CLyRTwe9nTJsab4UloleszMvDB6XwbQWoNL+fsRKJp8STXFM1\nS/vzeWHNqO+Xl1sUv5pKDdhCsqOkEWY+diYYLKlpFH5B7dcVftSft8Kfrv0ZCn+6iVf4kVIUNtM/\nTxQJHyxROUEnTMWmpg3azkjhGy2dPAhfSmEsTDij9o/6TIpHQUanzyfoBiYVM6cj/Nj47ANXfj//\nn70vj5ukKs99Tu9VvX3rMMMwMwgyMIOIAoKIJEGviRj3GzXRmxj39UajNzH5aRTjNTcquF4F0RhN\n1BslRkHZjIpRVhlHGBnZhmH27Vu6u7q7eu9z/zh16qvurqrznurvG3CY9/ebH3zfV8vp6ree85zn\nXU4l5wB+EMP3SFIqwIyxGGbN2SXAD+l2KMefY/VoDN+pIq2k+qOTlRy/4zuycd2yMvx4HBkjNnCY\nlsnVLfeJX8l76sqZw2nJR0PD71ijz39MScetNJcsyW//zuVoHqhhxwEfWJZl4aJzWVXQlspyJo1J\nVNvVwRhECOBLp4k6fgn4IyxtiOGr2sNKG9kIQhW05TXUozLkahUVB7R8GT7gyjphRN1rA8VXchYN\nYfgmt6MBplPpaSV6gwFPaR7ApwKOfAauJBjm+wBiOROZqLtGuUV79ijZkYONyPDd8YdpKcvA8HsM\nsNoBGWqe++sEbdu99lKluYrsOO/u0dDxn1iAn0qN7hwPLEuWTiknsixGADMgaEuRFYCh8SsYvjMU\nffOMn7KsJTF8HUnHDdqOwfCdoOcIaA6tsCgMHxgCfFV5bjYLg0es9pRFY7HO6OpE3rMx6JuqCSsZ\nTyKXytHIDiD8J2rzPcnwuzUl4OvImYCH4Tca4r31Y8jLIElZpsCE5QzaAp60ZAXgH81tDlcc8Blj\nuxhjv2aM3cMY27LS95PmC/gEwIzqNJXJkCwReX8IpzdNUUQZZvLlGWBpKzX+Ws2/WyAQmeFPG5qS\nDuqo2yHVUGFWq6GSBsykiWR8CBSWA/BVgJnNwuxFbL7nvOWVWFsp6VABBxDf41EB/FoNfQaUuz4J\nC3KwEVa3wBDgG4Z/tVwsBnM0+5Nu9TrKU2JAFN8HaBo+4ElLVsR/jkVJ5xLO+dM45+cdpfvpAf4y\n6IBWPiBLxCdoq2I4gE8/nRWesMqmT7dAIDLDnzFnYHfspUwLAstptZh+a4t+3wl6+mQYAZEBf9ac\nXdqPQNViM5eDEbXS2XmuFlrLJukAmoCfzcJkjcgTVjUF9Hl/dHUrBxuR4Q/4fsiHDth6mWa1GsoT\nohhzxH9iMfHMhhi+aoU1wvDDxu+RY49LOmNYNplFnMVpgJ9Mwkj23MO0zZMWqJIUqIDvu6xdScB3\n0gJHWKYPy6EGbQGH5XBO1jG1WY4zrkqiG8yQAW3An8hMoNqqis3AKYAZdZtAt7VzU8nwqZIOEAD4\nflXmgJulFnl161w2cPyaDDmfyiPO4jTfB5DNxwaur2VhCQvAQKV5vS5U4eFNz4btCS3pAOAAfsgY\n+yVj7M3Df2SMvZkxtoUxtmVubs7n9GjGGBt1+hCnMZzdqiIz/GxApWQ8LrzEs6wlMfyjLOmU0n0U\n0oXRtECfLB2qpAM4/XScwGR4pW1EwA/a3lCaB/A7HZHpQhl/MVMEB0e1VSVp+KK1RYQYhGT4PXvZ\nGT41aDtWHUe9DsvZjMX3+Udg+IwxTBqTZMA3nLYUkRl+wWe3K2menvjk+JU51C12pchOBDsagH8R\n5/wcAJcCeAdj7He8f+ScX805P49zft7s7Oyy3lgH8GP57FiZChVTAGXgS+txeorTaEk6yyBJlVO9\nYIbjubCOpAM4DF+FVONUS7rbG7aUDJ+y+Yk0ea1Kq6KWdJygv2x9rWX1OroxoN73afwmx9/rAZ2O\nFsOfzEzqSTr9iEFnT5Wwr+9H0PABscIlkR0AyXwGSdaJ7vtBCQtysB7fp062Aw3Uwk5MpZCNiQyy\nY0LS4ZwfcP57BMB3AZy/0veUpgP4yGZhxNqRdUzLiCHO4jCTPl/sEEujOM1ILnLY+ONxmE7zKm2n\nd+rdy4kAwI/K8L0sRwX446SmudsbtpQMXwvwnWtVmhUaYEatg6jVlhiyYsIaS8NnLLhaLpeLvuNb\nvQ6rIDQd3/EPMfxYLFhZ8tpkhs7wkc1G3/GtVkPZDEhYcK6tW4MSYzGRtCDTksPGzxhy2TF3fNOw\nFQV8xliWMZaX/w/g9wHct5L39JoW4Ody0Z2mXkclw1BIFwZ7iUjzOD0V8GVqXalZEnJIqxU6fjPL\n3Ovrjh0Q2xuGBj01Gf6ApKMB+JElnb7P9oZAZMCU1yo3yyTAj5zW65FEAleHzoV1NfxKs7IUgwjK\ncgGc9toRu63W68HxKznYofhPWGtqaQOV5pR3N+qOb07CAgMjSWoU3wGc4qsGgeFjhFOtqK00wz8B\nwK2MsXsB/ALA9Zzzm1b4nq7pMnwzFt1prDT3dxhgxGkoLyzgYTlh3Q4dy+bGBHzmUyUMLJXHR6i0\nBYiSzjiALyWdXp0M+JTn7zL8VoWm4UeV1JyUUu89B2wMhu/GIFS+7wJ+tBiEzFALlHQ0M9QAPUln\n3BhEOS3GPtALX5rn3aX6PjDUXkEB+MlcGslY96hIOop483jGOd8J4OyVvEeY6TJ8g0dPTbOSBf8X\nFhjQMSm9XKS5Tk+gdmYuYqaCrJREE0/zY/iAu6zVCXqm4inkU3nB8BOKJiTjaPi1GjoxoNEPkHSk\nfhCR4Q9IOgoN37mNnlGyXJwL60xYcvIuN8soUgAfNuw6B6BZC1Gvo+LUcAQGbZ3ghm0zsu9rSTq5\nHMwxCt/KKcN/dQuI+x4UbdZtW73bmLRpcxo7FnfAPTHsg+dyzgZAxNlwDDtm0zIBTcAfZ2/Meh2V\nRDec4WtKOoCnRTIB8NP5FBj6kRgmELC9oTTnpaU2j5I2bU6LZa2qzWAmg2zUSuFaTRswtTT8Fl3D\nB6KtsCynLQRV0qEyfABLhEHh+zLorG31OiwzjhiLIZv0cQzTdIPOOr4/ZUyh3CyLbSZVy+Ixg87l\nZED8Cogs6UxlppYSLgjjz8XG2A9Cw455wK936qIfDQXw+xGKZ3o9oNmEFQ/IAwdGcqm1JR0C4LN8\nxBhEvS56ifRt5fip7WGluf10VEjLGLJmxMBVtboiksgAw1dR63G6rdZqqDh54NTxU4KeA4WHVIbf\niEXKMrKMWHD8yhMD0gV8wDPhKhh+llf1NxHpdoFWC2Wnl7+vDWUZUclOIV0QY5cd78I+eDaLLLOP\njSydx9IGeuJTWE43QqaCLPyJtYMZvqNjquqPhk1H0hGBq2iAX3OSNwIlKWeFosvw3Z7+BKSNHLiq\n1VBeAYafSWSQjCUHGX4Q0o7L8HOKoCfgMvyw2KvXBgC/2SQBPjCwdQDN6nVU0gFjBwbSerXIjre9\nAlXDr/U1Bg51wgIQmeEXM0XU2jX0ak4LVQXgf/ekv8Dll1MHHt2eEIBfbhCWtYVCtOIZtzQ+BPAd\np1E1XRw2t0UyGfAjBK5UkgjgshydPGpAgIDVsmiA7wSdI0k6YRpyPC6abmkCPmMMxUxxScMPQ9px\nNPxqdWnzFsKERQWcKAwfiDhhEQE/CsPXAvy6JuBLOTMopReIHLSV32W14vRjUgD+pt59WLeOdu1x\n7IkB+NU5URFDWdbqLgtl8ysElMYDLsPXARxAsJxGt4Fm3dm1ayUCV6q0QHlfTcAEhNMPSCIhJyby\nBlKxTjTAD9reUNo446esDsdh+JaFSi6BZCyJTMJnBeHD8Ck2sM0hUcN3bqNn9ToqyV647zsX1hm/\nC/i1OSG9EJ5/1Ay10HdXAj7n2gwfACpEwD8qAj6eKIBvOQ9dwfBF4Eof8FtxoMU7SsDUyaMGPE2k\nqnPqE8cA/FANXN7XtrUZfjFTpAU9nYtmo6TFehmygqXpBD3l9dy0TFXRXlTAtCxYRlytgWsy/EK6\nAAa2tEJcKYZfq8GKB/TyByJr+G5rEevw4HX8TDL8hmaGkdPp0wqq4QDcAbetJrpdvecPAJUa7d09\nWpvaHtOA7xbP1Jx8WArDjwCYVQpgRmCYrtPX59Un5nIi6KzbU57C8IckHR2nr7Vr6NmOM4dFG7NZ\nGKwVLegZtL2htHFXKKpc2ngcZko034vE8A0W7juANkOOMRFIXVFJxwlKWfGAXv5AZA3fZfhVAlmL\nCvj1OupJgENRQwPAXhTBDV1Jx6o61bYqhm/bosByhe2YBnyX4VMAv1AQTtPUzFTwFM6EAmarhUat\npxyG19zAlSzRVmUqoK4fuKJo+EOAqa1jNioC7P02n5GWzUaPQTi9UCiSlJT0KTawQlF8aYbTXjoK\nw6+kefizB7QZMuCkJbf0AF9r/I7UUWFtFFLLq+G7vk9kyCZsNFpxPcz01kAoJlwJ+NqSTp0I+EDE\nVr169sQA/DoBMB0dk3OGdlvjJt5ugYqX1i6LC+sGrtx8XoLT1yNkKoRWSsr7RpR0AKDSLKs/dFQd\ntlpFxYj7b34izQP4OoA5EINQAL4sfIvC8K1kXy2JRBi/W4eiAvxMBkZM+KbW+FW9/IEBDV+nyjwV\nTyGbzKJEBMxIWUaePkaq519fbMlbkcyVdGzn3aUA/lHQ8Y9pwM+lcoixGMq2U7FHYPiAvtNLlqBy\nmka5pRyG11xJp1UeuI6vuZkK+pKOUgMfKrzS1TGtdlX9oXM5GFH2hXVWKIGTLTAe4BMZfjKbQky3\n8I1zwfATAa2dAdHWgjFtSQcQLJkE+Ix5iTjd6nVR5YwQSce5b8dqKNPRh22gnw5hdesMiW7e+JVC\nw9cla24dB4WsHQf85bGRnvgroWNSNXDoO427rG1rAH6EwJWVTQRXSsr7RkjLdJ2+XaUx/CiFbxLw\ngwAHiAz47iYoDfWJLJ+DGW/qSyL9PqxYSJU2Y2ONv9QoKRvvARFXKDq+X+l4fyTZpDG51E+H4PuA\n5vh1GH5ZjF93dWu1LPGL4wz/6JgO4EfKtKBmuQBoWB3lMLxWTBdFpkWnOnAdXxsjcFUxQ7JE5H3b\nbdSrfcRiwV12R8YvJZ1uTf2hs9loDbyqVVSS/ZVh+HITlE6dtkKJae4LawkwqCCgl780T5aRDsOf\nyEyIGhR5jRCTgK/r+0o503ngjUqbMowBK6QLYnWoOjEq4Oto+FYXAN1/jISBRCyBCgXwZUe544A/\nvk1kJlBuOw/9sWb4mk4Tj8VRzBRR6tYEyoYFPSXgNzW/Uk9pfKB5xm+atEpPwCPpdAlN9OUmIrqA\nX6uFSyLAWJIOIDpxKpFqYkIEDnUA07LAAVR4SFogEJ3hpz1kR9GPwXB2fVp2OVP6TrXn/ZFkxXQR\nVsfJ8FLEIEwM7gpGMg2Gr7tCYUy0W660aZW2AI4D/nLYRGYCZQpDTqdhJsSXqg34TvMrZdDWAXxt\nltMjRLscwO/2Yuh06NeXTq8EHIiXlrqkBTyA2SdQUxm01YlB9HpAoyG2N1whhg8AlT7hxGIRJtcM\nOlsWGkmgh5CgLTAWw692aujGoGb4hQjbBKq2NwRESlQ8jkY1mu9XKIDPGExD+I32hEVJ6QVQdyYs\nXf+3us74KYB/FHLxnxiA3yU4DSKm1lkWKsUUUvEU0ol0wIUdSacWjeVU+nTAByI4fVgvf2AJ8Gs9\nrbG7DL9P6Akdpae53PwkaHtDaYYBNJtarakBz4TFFb1oAKBYhNGv6/uOCjABwDDAbf0JS8aArDTU\nvj8hBqLvO+J/VSvEyAy/R+sJHTXobOUE4OfTAX2P3RVKf+A+FCtmiqj0bLEyD8sFPs7wl88m0hMo\n95wHqdQxI2wiUi7DyqXCAUc6TU3faQrpAiyuDrqNA/hWsh8OOFKHrfe1GJqZNBFncVRAGL9nX1iy\nScDnzeDmV8D4DJ8y/okJ/V5MlqWugQAA00Sr3gXn+kFbAChloBx/ophFEppbfFLkTAAwTTScPjfa\nDL9PK0+PtONbrYZKNoF8Ku+/+YnnvrITp+67664Ow3TQ44C/fDaRmUC5T2QJOdGESxfwK9kEiSE3\n6n3lZD9sxUwRFgVwPKlp2k6fCCmNB5YYfp1rObzbgIzRAF87BiE3PwlLCwTG1/ATil4ugGD4aLir\nOJJZFg0wDQMNWx8w3ToUAuAjn9ffJpBStAcIhl+PBphtdNGKY+UYvhlX+w7gjl9X0qnwJil+Jcez\n0vaEAPw62ugQdEwjL3RMLZZTLtODng5gUoOegMMSYgTATKVgxkSev24ushXr0DR84gbmXiukC7Bi\nhG2yHIbf6zF6DKJapQGOYQDdLmybawGmy/DTUI/fCdpqVTqrevlLMwzYmm0tgAiAz+t6MZRymTxh\n6dZwAJ7nTxh/Nh8hrbRWc/eiDjRJ1pyVG2UvAmkuWTsO+EfP3J74BlNS60iBq3KZlgcO4TQ6gAMA\nhVQBVozAMKMErjgXOiwLae0MLE1Ymho44LCcOGH8USQp1X6w0uSEFZXhUwBTMnwdwNRh+JqN94AI\ngA8bts4KpVSClUsGd/qUZpouYOpKOoATg0gHxMfkLZx3V7vwSlW05yC83WD6ZC1VQIW1SWQNicRx\nwF8Oc51+IqP8tswJkWCureGHlcYD7gwunUbHipkiKvEO6U3RBvxmE+0YR5MRslwANKKOP0loMxil\nxTBVUogI+O4mKISgJ4pF/aCzZS318leMX9ZXaAVt5b62RMA30HCzaUhWLqNSSIXXcABC0mnqj9+d\ncAtp9bsbhazV9KoYiwAAIABJREFUaup3NxYDMpmx3l1uqsna0WqR/MQB/KK6WkhmKmhLOomQfuDA\nEmASkj2GrZAuoBnnaJvhDAeIELii5CEDS4DZZPrjT+ZgpaD+4FFaDGsw/A4S6Hb1XlrGGIrJnABM\ngqRjoIFGU4MCWhYqRTFjqcY/DsMvGYQTJcOvakhSpRKsbDLcdwDB8J3nEonhF9TvbiqfRgw9/Syj\nZC/82QNiwm3GtH2/mC6ixzgaOYIOlM0eT8tcDnMBP692muREFnF06U7TbgO2Hb69ISCWa6kU7GYs\nkiQCANVsQnmsNuBT8qiBJUmnFdcffyJH08CjMHwNDd+GuL/2+ONZsqRjwobd0nilLAuWkweeTwWk\nBULc226JlYDO+HOpHGJgtBWKK+noAX7FjKkB0zRhtxLyf8nmtifIqbMcWD4HE5pB53odVrwb3OlT\nmmHAbkV4d2UMgoA9xwzDZ4w9nzH2IGNsB2Psb1b6fsPmAn5ODZisoOn0lQo4RLfAUMABBMtp6bME\nt+ueGVcea+Y1s4yoedSS4UcB/LhJA8yokg416BkZ8E3ahCU1/HaC3l7b2e0ql8ohHgv5fg0DDWci\n0fEfxhgKLEPKw1/aD0IzaKsKegID49cJerq+TyA7IgakuQFQrYZKTJHhBTiAn4iUsADAbd8dah//\nOPD2t+vdIIKtKOAzxuIAPg/gUgCbAfwJY2zzSt5z2OSXWc6qAdPd9apKTBMpl9FIAl1VpSTgspyo\nTiOreUNvoQv4HkmHpIG3I4zfARyuApx02m3RqyXpEBl+A+L+2oDPDHEPSqWtbotey3L7GIWaYcDu\nCpar/fyRpk24UsPXkTNLJVipkF7+0kwTdjsBw9DPUAMAi/LuuhuZE4PO/T46zToaLKRxnTRn/FFX\n5xWTALMvfSlw8cV6N4hgK83wzwewg3O+k3PeBvBvAF6ywvccMHfnGQJguizHIgauqGlpAJDNotGJ\n6+uA3tQ0hWkHrii9UADAMNBFHJ1eBIbPMujEgWZGwXIY05ekqlWX/SnTAqMyfGQEw1clYKfTMBLC\nb8igWa2ikmHhRWPAeOPnaT2Gr9N8r1RS13AAAjA7yUgaOEBb3bp1HBYR8BsNEVuCgiwA4vl3kpEl\nHRL2HCVb6ZGsBbDX8/M+53euMcbezBjbwhjbMjc3t+wDyKVEJ7qKQXBkuesV1WnKZZqkALhOr83Q\nHG3XUsds9bOMqJWSySQacTEO7ZeWixtU0mqpQDtoXquhnE+Eb34CjAmYKRrDR4QsKctCOc1JgC9X\nKNqSYD+JSoaJrb7CTAJ+kwCugNhYvFYT2xtS5Myuvu+nE2mk+gxWhvDuuju+Ed9dqu8D7gorsqRD\nGf9RspUGfL9POvDmc86v5pyfxzk/b3Z2dtkHEI/Fke/EYKUJD10ua+tEp6lU6E5jmrC7KX3AjAsv\ns1JqwIzls8igQY/9UAt/ANgZsfuWttP3BRBbSXVcxJxycp51NPxsgsbQHMDXfv79JI3hAzB0Wwxb\nFirJ/soy/F4CFoXsOIDfaBMhoVwWnT7DdruSZhiwecadEHWs2Im7Phpqcse3KvEeXjmQoOFHmbAG\n6jgeJ7bSgL8PwDrPzycBOLDC9xyxQidGYpguy6EWz3gkHRLL6aUiAKZg7RUCYGrverW4SJ6wbGMa\nQBTAEYBfSahlMnN6KV+eZNUqLUskk4kOmN0Eqmmgb6jfWjOrWe1pWSgnCAx5HIbfidMYpkN27E6S\nFnQuldBKAB3QJJ0GDBgZ/U26C50Yiexod1vVYfimCbuXjpChJkgC6d09SrbSgH83gNMYY09ijKUA\n/DGA61b4niNWbDMSw3QlHeoL61TZAnSnicIwAcBKEFYduoGruTlUMmL/0NBKSQB2SrBQ7QmrKyQC\nK64GfGNGvCB6QVumxfD1AT8OzoBqXP1MZWsOkv90OkCjgXKsTWb4sRgnbz4jrdCJwaKQnUQCZqKN\nXp/YXttLdihyJkyYaY0qXseKLcBKaZCdKBleFP/pZ7Tf3XxP+AMJe46SrSjgc867AN4J4GYA9wP4\nNud8+0re088KTaCSJDibbqaCk5YGqJ2+b2TR5Bl9HbPdR7IHUW2rMun01BjE/DysQlo9WQFopMTn\n056wOsLFKky9M7y5SsRb9F5aTkuriyrptMT3W+FqpzCLYnIm+U+16koiVA3fSPe1slwAQXYqSRrr\nNdMCmEjPv1SipfQCSwyf8g4OWaEJVHTIDrXwrVSiT1gO4Ou+u/FmC7kWbXV7tIyQIDqecc5vAHDD\nSt8nzIpNjhKBobkMn9qxsVxGZcIAYCudvpmJxpBZs4lCC6Kfjsqk01fpgF8pKFo7OxaV4RfbdMBP\nrZoQ1ZJVACAED53tDTdoMHydboeAA/gJLG1VF3abokbQ3Nn8pANFlTbgjl8wZGJQ1bFCC2gmONq9\nNlLx8OWBaXCgLiasCcUcNACYxPFPpvSBr9js41HC6lB7xzdndQuoJ6xe2kQL+oAP20axBVRiOjsS\nraw9fvKFVtAKjT6NIUsNv0V8qcplWAXh9aGVkgAaSeFUugwTjQaKTbHJh9JcSYe4hJyfh6Vq7eyY\n7YxfW9JpCnZpQZ2czmamxQprkbjEclo7KwEnnUYdYvWgDfjO+CutivJYmSVFZfhlB3Coko4ZCTCd\n50+ZsEyNtFhNObMBA0ZCH/gKdp8GmLrttY8cIUs6jYi+D9tGsQnRLfZxYsc+4Pd6KNp9EsOUxT+N\nNnHhUy6jkk+q0wIB2EnhVNpO02gIhg8NwKcGrubnUTEIQU8Adnw8wK9wQjXS9LQYf5nwWQEB+HFC\npSRjsBPRxl90+tBXmgTAl0FnSh2HZ7crsqST1Af8QkOMnwL4Wj3lPQyfFL+CCTNBeAe91uuh0OjD\nory70veplc5zc7DMGBKxhDp+JX1HN+jsvLsVAtk5WnbsA76URCgMGYCZ6sLu0AG/lIu7XQnDrJFw\n8tjT+k5TbAEWBTB1A1fz87BSiu0N5TCc8esCZqLZRrbtbASuMhfwaYyoU7fQUHX6dKyeKCId7yjT\n0YdtwhbyGIXhG1NOk7wS4buyLJfhKyesbNYBTH2mWJTjp0xYOY0so3J5qdMnMWhrxDUBv9kUDJm1\nwVUo7qzO+zyGNuU2c3OoTBgopovhnT4B2E4NipnUfP5S0qG8u0fJjn3AdwDTRgednvoLMzM9tPtJ\n9CgyeLmMskGolISHJcSJ7FWaZAl9wlsoi08okgLnwukpkgiWnF5bkrJtMeG2qupjp6fpLXrbbXep\nT1uh5GHqAg6AotNmgwSYM06TuUU9wFf6TzYrGH6E8Rfq4lmSGL7TmoMkSZVKsCaEM5B66cCI7Ps9\n9GF3FP6fSiFrikmBVIdy5AisfIpGduJCDtQevyPpuNs0Pg7sCQH4Bed7qrbVoCPTrUlOXy6jlObu\nZtGhw3CcxohFc3qrRxiQw3LqDcLXWq0CnQ6sWIem4TMhfkeRpIqdGIkhY2aGnlbqafxGm7ByMOP6\nTKtYFSBLYviz4jtuUCQp6n62wBLD1wUcAEVn8iSNP6+xiUiphFJRfAGqCYsbjqQT03z+DlkDiBOW\nTtB8bg6VrGJ7Q8fsmOP7EQBfvLs6Hd1W1o59wHdmWYDI0nR0zHIZ5WSPxvBjDktgmrO9DNp2Cb2y\nV6+mB67m5520wCYNMOX4owSuOnEa4EuGT4lB6FRKAqizPLIRAD9TbSDZZyTfSU4XkEAHdoWw9Ndh\n+DLoqQuYAApVAVIUwMwWNeoIymWUCknkU3kkYuESaDthgiPm7ndANg9Z0wmaUwFfuTWpYzZzyBrT\nfP5S0qG8u0fJjn3Ar9ddpyGxBGoDr04HqNdRirdpGj5z8sAjOr3Vqal1zGwWZqoHmxJ0np9HIymW\nyySnh4kYetqFP2g0UOglSM8ehgEz1qRryNSgJ8QKRXuyBcDsBor9FG3Cki2SKZKUDuDH45HHX7SE\n81MmrOyESDyoUzZBKZVQysbIzx6ITnYA4rurU6k9N4cKpdMnsFS0F3H8jV6TJCcfDTv2Ab9Wc5eF\nJJZABfyKuFaJtUiA7zoN19zkwFnWdvodtHrqJaWZj6PVI8Qg5ufpjd8AwTDRAINmPxTbFoBJABwA\nYsKirFAOHKBLIhDPPwpgwrZFAzUK4MuNzCmAX62ikk+p94N1rMFMGITir2ErlAVikgBzUjhEvUSQ\nLkollDKMJmdy8fkMrilteBk+ZXU+62wlqloh2vbS5icUssOd1tq6/uMwfICGPUfDjn3A12X41J7y\n5TL6TGTPUFiO2wtlpZ2eWu05P09Pq4NwehM20NKPQRR5isbwARiZPq2B1/79WhNWHSayiLCjUL0u\nWiRTJizJ8Cl1EJaFcj6JicyEMksEcCYs3fF3Osi0+0iBJqllp8QDtUuE4HC5jHKa08hOT1w3CtnR\nendPEIkF9oLC+Z2uvBXWppEFCfi6z9/R8AHa+I+GHfuAX6tpafjZggB8ZeDKkRQ4aEFb12n6mnpe\no+GW95Ocntpx0lNpSHL6fkYAvtYOGWIgBZYmMxzTAOyOeks77N+vN35uwNSdbAHB0mIGbfxuLybC\nKsiyUM7GSWQBcMbf1wQcx4kLLKMlidRVabGcCw0/0aExfLmfre74PUFb0up8tSAu9sFy+IFzc2Kn\nOt6kkZ2+cDRt//EyfOIKd6Xt2Ad8TYYvA1dKHbNcpmuwWHIao6cP+AU4HTMpTi91TNWydn4elrMT\nD83p0wLwtfaQg3hpYaDWrqHXV2ffmFnA7hL64e7fj8qUkMko46/3DGQ5ITXUa/2+GH/cpL2w8TiM\nWIs2J1oWKgYjrU76faDJMzB0yYKzKXYxZpJ8P1bMi/baqqBztQr0euT4lXQZs6f5/HUZ/loxFvug\n4ti5OWenOsIG5vACfgSyJveDOC7pHCXT1fCljrmgiMhXKig5OemkoK3T5jiS00M4HMnpZQOyw4r7\nzM+jMiOAkqTh99LRGX5MPChSWmw27j6rUNu3D5WpLKnKGXAmrAgME3A2MqeuUBId2JS0WCdoSyEL\ncstEs6vpOw7gFxLE8efzoo5D1XyvLBh0CU09wI+wutUia+vEng31w4r7HDlC7wMEoNGT767m+G0b\nE0z4frmpWHUcJXtCAL7RAeIsTnOaSfHl1hcVWnW5jJLD8EmSTjeNBDpItiKwBCZuRNLwpY65Zz78\nwPl5lKcFQyZJIt2UyDDSBfxGw+0LTnF6s5BAAyZ4T7HC2r8flYkMaeyA0JG1J1sHqYrJPHlJbiS7\ntBiEZaGcImx+gqVHbkQE/GIyT9OQV69GFnV10LZUQicG1HmLJunI8Xc0dexGA4k+YCYMmu+vnwEA\n2POKVejcHL3TJ4TvM/SR7ugDftEhO8clnaNl9ToYE0tnkoY/4+iY8wpg05R0Gt2kAMwIkohkyKQJ\na60YS31fKfzA+XksTorrTpvTyuva3WQ0Sce2MZFwtpkkPH/ZcbJ5WHHs/v2o5JKk1QkA1DspZHua\ngONo4MV0AVbLQp8Tdu1KE9NiLYte5SwZckcTNCTDTxMnrJNPFoV7KrJTKrmrW5KcGXX8coWVKtBW\ntycJhk8J2lZy4jsiSTod8e6ypv7qdsIpuDwu6Rwtq9WAXA7FdBFWmwCYp50IAKgfUHxB5TJKTndB\n0rK2k4iugTsMWUvHPKBg0/PzWCgkkIqnkE2qW0ja7WQ0SafRwETK2dtTp3hm32LwQa2WeGkNwuYn\nECUTnX4CZrcCWmctxyTDTxfAwVEltIcw0n00KL2YLAvlOGHzE3gYcjsa4BczRRrDz2SQTbbVhWPe\n1S1Fzow6fufEQqZI8p2M09tH2Xxvbg7lE4TfkCbcTkTft20UNFa3R8OOfcCv14FsFoV0gbYsPOtU\nAATALJdRnhBeT3ppW/HIDD8vt0qjAOY6wdaVGv7cHBazMUwZU7S0wHYistMXndbRJElHZhkdDPms\nB8QumZUUYfMTLA1ZO61UMnxHtiA9f5Org86NBjq1CmzWJfmOzBgz25qgIRm+MUlmmFmDqxMWSiV3\ndUuSM8dk+AXihBWLAQZrqCesI0ew4MS6SKvbViwy2UkaWWST2eOSzlEzyfCpTjM7DQO2OvBTLqNU\nTCPO4silcsrr2jZEL5EIgJ/KZJFJEFPrZPHJXEiAstcDFhexaHBMGVO0YbRj+iuUbhfodjHhsEAK\n4BtOXKFxOOSz7t8PQGwsQeqU6TyKrNzdg2qS4ZsO4FMkKYPB7isA/6GHtPoAyfHnmvN6KxTJ8M0p\nWC1LXakN0TGzbitgwSPpaDH8pkJm9DsxnRZyLDlo3oatmrDm5rDodDadNgiAbzNRdBWB7MA0UcwU\njzP8o2Zehk9lOYkW6iodsFxGKZ/ApDFJYsiNBkS3wwiAD0O0cdXqBRQWuCqVAM6xmOyRAd+WKxQd\np3eOnTAEi9WqlgxboTiAX0ZDTwPXZWkS8LMCFKiV2g2eCQfmBx7Qiv+4E1bfAq33r2OS4eem0e13\n0eiqP3u2mBDtwZshWWrl8hLg6zD8libg2zZgGCikaRo+4LQ3V6Ukz81hwYkVUfxfkLVWpPgVTFO8\nu8c1/KNkXg2f6DTZdBf1klrHLJu0XiKA893HW8RWhB5zAL+QLpBiEC7gh/VknxcZPAuxFonhAIDd\njLCsdV6QgileKpKkI9NKw1Yo+/YBACrdOq3K1svwdV5aKenkRfYHieHn4mjCQN8Oef6agO/gNnKo\n6fmPBPy8+I5JQf+pNOrIArt3Bx9UKqHkBPypaZkMfaRsTZbrITtkwE/3YDeYKF4Isrk5LORiyKfy\ntJRe+e5GZPgTmYnjDP+omQP4VA0fENWe9TonsBxGcnjA8d1EJzrDJ0pSLuCXQ5igA/iLsEkMp9cD\nWi2mL+k4L0jSzCGbzNIknRnB8BsLIffZvx+dnIFGNwLDr2qkNkqGn58FoBd0bu46FHzQAw+gsmG1\nuLbuhKUL+KnU0gqFtMIyBeDv3Bl8UKmEkk78qiE2D9HOcvGQHeq7mzU56twQq9iga9ZqWDRo+r08\nxUxEAHzPu3uc4R8tcyQduayi6JjZfEzt9HNzKKdpedSAM9knowM+1emTSSAR64nimaDPKgG/VyMB\n/kDQMwLDlyyHBJhy16WwTUT270fl5DUAiGl1UQFfMvzCKgBEwDxFALl957bggx54AOVTxPi1GX5N\nIxfcQ3YAIsM/IS8a/YX5vtMa2UgYSCfUVdHj+n4xXUS1XaWlxWZjYvyHAiZcp4/OQrJLX93agJHo\nHmf4YcYYu4wxtp8xdo/z7wUrda9Q8zh9t99Fs6vuaZ2dTArAf/hh/wP27gUOHxYMn6BhAo7vpnpj\nOb2WjtlNAlbA8XNzaCYAu9fUAnwDzUgavmQ5JEnHXaGEZNPs34/KOgHC2kHbKAx/UoA4qQGZTOu9\n6z7/A/p94MEHUT5JyERaGn4Uhu/ImQBx/KuysJFF/5FHgw9aWEA5G9fz/WRXZEiRtpLznmi4kzpp\nhVuI0wA/3qLHr6JOWF4N/wmSpfMpzvnTnH83rPC9/E0y/IyG008b4YB/220AgFKiS5Z0bFu0/tVy\nGs4FQOXzekHnTE+M/+BB/wPm57HoBN1oWQriv9pOP8TwSZKOM65GmCS1bx8WTxRASQ26AdEZvlGY\nRiKWIL20uQmnF9OvHvI/YM8eoNFA5QQxfsqEJUm9CTsS4OswfNkevPHwPv8Dmk3gnntQmjb1fD/t\nAL0uYTAMd1IsNdRBX7OYJAH+IhpkSUe8ux29sQsddMD3KerCStuxL+lEWdZOJFGPFYIB/9ZbwXNZ\nlHs1sqTTaDgbmOsCZr8PFApaLME0RTtdma8+YvPzWJwUGqwWYKZ7kRk+WdKRDN8K6Cnf7wMHDmDe\nCe7OZmeV13Tz2GEHr3r8zLaBdBoskSBnWmSdGrbafbv82ewDDwAAylMmGBjy6bzymvW62Gs5Bq4H\n+PW6m5IMELvFOuO3dwYA5h13AM0mSlOm5urWkWN0Y0CG4U4spBXiZFr4/uHD/gccOQIAWOhWtSSd\ncXy/mC6i0++Q1IWVtpUG/HcyxrYxxr7CGKN5x3JarycYiXdZS3R6O5EHduzwP+C229B41vlo92jd\nAgHHaTJ9vRdWstF8HpNO8Qyp42TOWdaGMfwTxAS4ooAvT3ScXo/ht/wzLebngU4Hc06B1ow5Qx5G\nJEnHmYGogbecU5JRa8ZdcB8wCfh50RYixtSvYL0Od4PuFdfwHcCv75rzjwH95CdALIaSQcvQATy+\nD0Ri+HJiKRHy+M1CEjayoQy/x4By29KTdNL9aIDvMHzg8VFtOxbgM8Z+xBi7z+ffSwBcCeBUAE8D\ncBDAFQHXeDNjbAtjbMucs9xaNnPFz6y20wdKOpYFbNuG8oVPB0DTYOXqzshwPYYj2Wih4N6HxJKl\njhnE8B98UAvwXd/NaK5QhpxeB/BtmwM/+9noAU4O/nxBSCezpprhjyXpOIA/kZmgSToS8JEDfvGL\n0QMeeACYnkYlRtt8A3BwO8uXxkS1IcDXWWHVbbjB/QH78Y+BZzwDpbalx/Azzvh1/KdWA/J5LcA0\ns0xsqRgC+OVCEhycxPC7XVH6YGYikh2n8Ap4fPTTGQvwOef/jXP+FJ9/13LOD3POe5zzPoAvATg/\n4BpXc87P45yfNzurfnm1zE1vyOlp+Fmg3jdEcHb4S77zTqDfR+mcTQBohSdue1sTkQFfsimSjpmP\nw47l/Rn+r34F3HUXFi86BwCxtHyJqI/F8CtNdZZUIgGkUhx2ahL4538ePcDJwZ8z+kjGkrRe+A5G\nGtm4vqTjUF6qpOMCvjEL3H336AEPPACccQbKzTJZDqzXgWyOLf1ANQfwE7EEzCStJ74r6fhl6lSr\nYhJ7znNQapb0GL4ZAfArFX3fNwEbhj/gcw7ccgsWNq4DQPP9JbKjSdaG4lfA46Nj5kpm6azx/Pgy\nAAFpCytoERm+aQKtbgI9xIBHHhn84223iSXtxvUA6IUngBMQazTCi0K85gV8nWWtyWAnC2LCGrbP\nfAbIZrHwjDMBaEo6Bh9rWdvpd0jVnobB0Nj4VODf/32UkTsMfy7Rxow5Q+sD5CgzrJCPzPCp3VZd\nwF9/ZjDDdwCf2umzVhsP8AGQY0CupOOXlvyznwG9HnrP+T1YLUsrJdlwGg2SQZNz4f/FopbvZ7NA\nhyfRuWe727fftRtuAH7xCyz++SsBaK5udX3fy/CdldxvvaSjsI8zxn7NGNsG4BIAf7mC9/I3L8PX\n1PCBAFnn1luBpz0N5ZjIItFqfuVkQIQWdHktKsM3ATszBfzHfwA33rj0h0OHgP/3/4DXvQ6LvIFk\nLEnrlLnku9FYjifTgpqaaZ9yljj/mmuW/tBoiEkglcI8bFLAVg7DNAEUCvoaflSGf+JGYNu2we+6\nVBLBxDPOQKVZ0WL4uUIMYCyShg+AXKkdCvg/+QmQTqNyjiALOkWHpgR8Kmg2GkJPKRSQS+UQYzG9\ntN6FBvD2ty/FITgHPvhB4JRTsHDJMwHoZagZkqxRbShhATgGJJ0w45z/Kef8LM75UznnL+acB0QQ\nV9DG0PABx+m/8hXBbLpd0Wf3rruAiy5ygZci6ch3NC/VBypoRmb4gF1cA5x9NvDKVwL33CP+cNVV\nQpD8i7/AYmOR3ilzeIVCtaE8fIBYvGQCdn4VcPrpS7KOZQGXXipA53Ofw1xjnhSwBdzMXCCf15d0\nJMPXZMi1VacIf9myRQRwHn0U+OpXxR+jSDpZ5miNRIbf77tZOgB9heIC5uRJwD/9k/B/+T3++MfA\ns56FEsQkRtXwbXupoE7b94sisD2RmSCTHQCw/+pDgtx8/eviF9deC2zdCnzwg1hw2jRrrW5NtoQB\nFPPR8I91hv/Ym4fhJ+OiMlAnta7+ktcAN98M/O7vihLWXE68RBdd5H55lJfWTbYpOI+b+tJKp8/n\n9Rl+Iwb84AfAxATw7GcDmzYBn/gE8MIXAqedhsXmIr1TpsTtbEw/aJtOA7GYFsM3DKDRYMDrXidW\nVGecAWzYIOS0b3wDePObMW/PkwK2gAe38+NJOpRNUOJxMf7apNCJcfHFQCYDnHIK8J73iDGce66Q\ndHSCtjnoAX6jIVitl+HrkJ0/f4c49w1vEGOemgLuvdfV7wE9hm/kRK96sv9UnPe0UHDvVW5pMPzX\nv1M8+ze9Cdi8WfjSaacBr3kNFhtirwWd+JWZ01yhPE41fMJODb/F5gF8IILTf/hy4F8+KEB/+3ax\nPE8kgBe9CKW7LwegB/iyKIfs9PLEQgGTcQE0VB3TtgGceCLwn/8JXHGFmDzOOAP40IcAAAv2glbh\nCeCwNF0d05PlAmhIOjaAN75RsDJAgM6rXw085zkAgLn6nBbDdyWdXbv0xu+RdDg4au2aMlCcywE1\nlhfscs8e8cupKeDcc4GzzkInEYPVoqcFuisUHcAf8v1iuogD1YCsLY+5vn/qU4Er7gV++lPB7CsV\nsTp83etQavwGAI3hO/vAw8xrAr6H4QPQZ/ituGD4H/6wkNJOPx34n/8TSCSwYC+Agent1uV010S1\n6k5CtBNNZJNZxFn8ccHwj23A90g6AD2X2nX6OsSX+4pXiH8eKzfLyKfySMTUj9CVdCY1Ad+yxMoi\nnYYBIBVPaQEm5wA74wzgS18aOWaxsYgNExtIw5DDzeSTkfKoAWiV9wuGD2B6GvjWt0b+3u13UWqW\ntBh+JElniOEDgqWpAN/F5de8xvfvc9UD4OBYk1vj+/dhi8TwhwB/MjOpB5g2RMzgkkvEP4+Vtt/m\nXpM6DNf3qf7jkTMBMblQ5UzAGf9Za4Grrx45ZrGxiEljklQD4eL2tJMvXC4Da9cqz/PGr9wtVo9l\nDf9xYT4MX6vaMKylfLNE1mBdhj+ZVF/Ya5YlHJ4xMMa0XlquaPYpNXyKuVkuWVNP0hmX4QfYgr0A\ngFZ0NTAMXUlniOEDtAkrlwuPrR6qiZTBE3InKK/F+RDDpwZth3x/ypjCQmNBmRbr5uGHzCs68StX\nzpzS9P2H7n2uAAAgAElEQVQhSYdaxzEA+AG20FjQqrIFhgCfYp4MNQDkwsOVtmMb8IcY/pQxRZZE\nvKf7WalRIgetIju9BHzHIrGcAFtsLGIqowf4bpYLtQGWh+EvJ+DP26IgiJql4wJmlCwdH4avMirg\nr86tVl5LSvHZLJZiSBQbAvxpcxrtXht2J9z3YjHxlYX6vuODWvGrKKtbwJV0Iq1QAmyhEUHOnHEu\nTAX8gdQ2kFuLrLQd24Bfq4llqbG0nZlkh2FGYTk6WRbusnbGaSUbFfAzywP4rW4L9U5dqx+4YQCY\ndCa4CtFxPYCZSWSQjCWJ2wSGr/znbFGRHSlo22rRdo3qdMQ/D0MDlpfhUwDf3d5wTElHruZkwDLM\nVBNuuVlGKp6CkTCU13LDUBPOTDJO0JZAFiirc53VrUvUT3B6HukCfka0AHm8bHN4bAO+pHYx8THl\nslZlJIavUWlYrYohZJxdgrSydDyArx24CnB6+dLrSjqYcCY4Had3BsMY01qWhz2iuboAfO2gbd55\naSks323AsxT/AZaX4Z+QVUs6A4vUMQBfShhU/1eubjO0rT097aD0AH9Iw5/ITKDVa6HRCY8BUMja\ngq0v6RirHN/RITuG4WIPtTXHStuxDfi12hJ6Qzh9uVlGtx/QidGx5ZZ0nJYgYDkC/fCa0xpZ2nJJ\nOpEBXzL8oN2Ehq1UWpok4OiwhNQ6lfKiK+kMBG0BGuC71XKDDJ8yYVEAv5guwkiqGfIAbo+p4QM0\nhq8E/GYEOTMP8SypQdtKRQBmUsig1DoUqpypreGvdoiXjoZvLH2/xzX8o2GeSkNgKe9WxZJVgN/n\nfRyqHcLqrHpJDnhwm+KNXvOTdH6bGP7iokhHdIxa/FMoiHt2A+ZlKelQXlrOh2IQAC1TJ4jhL4Ok\nc7h+mCTnAEMMfwwNX37XVElTlbCgs7oFPP6v4/vFpToFaotkle+3e21U21Ut32cMSBczoqYkwuoW\nOK7hHx1zo3XCJECoWE4qJQpogt6teXsenX4HawuE9CwIp8/lsCyAX26WlcU/qtvIZT2V5YjSeERj\n+JNLwECVdFREfN6ex0RmgrQBdcvpshxZ0nEeppEw6JugEBg+FfBHGH69Hrx1pd+Jjv9LsrMcDH/e\nnifHf8YC/CE5E1CTtaVuq/5/1ym6ktcxTQH6mJigA7770guTO9ZR2puvpB3bgB/A8FU6JlNUse+z\nRMfGtXka4EtJB8mkmEnGyNLh4MriMVXgKgrDNwzoMfymsx1iBMCXHzkIl+dsetHVAFEfQ9JhjGn1\n07Ht4GSmQ7VDpJRM7zBcDV+VbyttKGFhOSWdfdY+nJQ/ST0GjKHhVyqDDN+gMXzRbZUA+Dqbn0ii\nPjFB1/CHVrdywqq2NbLEVsCObcAPYPiUZW2Y0++3RMfGkwp0p8/nIV5AVURSWsfZUm2I4QNqlqMK\nXB0VDV8e45V0iICpUl502yoA40s6AH1ZrppwdeTAEcAHaDq+JDtOYDWTyMBMmqSgbRgRb3QamLfn\nyb5vWSJuaZrQ0/B9VreARi+poNWt8+5r+z6gx/AXFkThoGM6Qf+VtGMb8IcYvqtjEjMVgpzGZfi6\nko7qwsMnASMMHxg/cLXYWEQilkAulfM/YMhcp89mxQqF4vQS8Mdg+IF7sNfntHLwgfEZPiBWiDJg\nHGbyu/abcO2ODatlRZN0wi7sd2Ju8PudMqbGZvj7q4LsrCuuU48BS77PGPQkHacXvjStfW3DAF/K\nmZqSDgCx4ogYv3q87Hr1hAJ8V9IhBq7CnD7O4qS0OjkMN9mG6vQDa2Fhugw/jOVMG9OktDrAk+zE\nmABwCsNfdIBliOHbHRudXnjHQSXg23OYMfQknXHTMgGR9y9TQsPMbZHsQ8QP18Req5GCtpT0MWkB\ngD9uWubeithjQXt1C4wVtNUBzDBOpSvpuPErQI/hDycsaNRxrKQd24A/JOkU00XEWXxsp99n7cOa\n/BrEY3HSMCI5/VAeMrCMDF+jU6ZnHwpnEETAD2D4gNrp5bPyA3zOuZB0NBn+AODrSDoehj+bnXUz\nhMIsDPB1iq6811gOwJ82pscuvJKr23UFOsN3fT+Xo/cyGmL4ybjYu4Eq6QQ9oiiSjptdSdXwWy0x\nAB9J5zjDX0kbcnrG2LIta6kMBxiSdMYBfCLDT6cFGQ+6zcHqQXLQsFYTWS4u4FNZjmT4PoCvcvow\nhl9tV9HutaMFbRMJ8fZGlHQkw1f1owll+HV9hp9MikBkJA3fYzq+b9v+G7PttQTD15EzXcCfmRHa\ntirLqN8XJ3oYPiAIz7itORYbi0jGkvpyJqDv+z6SznENf6Ws52w67GH4gJB1loPhUzN0ul2RVOE6\nPbV4xgfwXR1TwXJkbDjI6XeWduKUiVPUY8ASoYnM8Ify8AE64Pvhslt0FSVoC9AbqAVIOq1eC7V2\n+Pe33Azfxe0xNXxqaxH5kf3iq/usfZg2pmEmzdE/+tgA4M/OimQEFcuv1cSkMNSGWKe1SJDvH6kf\nIW+NCQyRtYkJwd5VWVIBciZwnOGvnMlvfAynD8vSoTL8ofoX4QQL6vv7AX4ulSP31Q5yertj42Dt\nIJ40+ST1GOAD+FSWUyqJmcdHh1WxHPms/HAhSlsFIALg1+ti/E4vFGCpslcl66gAn4HpN34DlkXD\nX2wskjtm+vnPXmuv9up2gOEDwLwi8D3UOE2aTmuRoEe0s7yT7PuAcHW3WFyOR+X/8v32y9I5ruGv\nkA10nVqycQNXVstCtV0lM/yR2OuqVcCRI+oTfQCfMSbaK4yRqbCrvAsAcMrkCjP8xUXxpsSWXIwq\n6cTjwXJvlLYKgAc0CwW6hu9W3AiTk4wqcKsC/BlzhrSPArD8gN/pd5QrlLDb7K3sJWfoAD4MHwDm\nFHEQH98H6JJOPh+8iN6xuANPnnqy8hrSBgCfWofiw/Bls7njDH+lbKjSUNq0OR7D183BdztlegF/\ncTG4b4C0IKcnLmuDMhUeLT0KYAzAlwxfpcMOVdkCesvaoL1KonTKBCIwfDlheUzec1yGT5Vz5DUG\nUnqB6JIOsdo27DY6RVdARIY/1ClTGtX3gxahjU4D+6x9OHXyVOU1AKE+2bYP4KsCtz6AD9DTelfS\njn3Aj5ipIAFzGNdkHrJO0GpgGKtWiYuqZJ2RE4XpNFDze2F3lnYCGJPht9vqAprFxRHA10mtCyLi\n8oXRlXTceZ8K+IcPAycMBrZdSUfB8MNiq7qAP8Dww2YSr3EeyPABNeAHSTp2x8ZCY+HoMXwfSYfi\nO0Gc5NGyIDtUwPclO0AkSQcQcRsZtH+s7NgF/JE3Xdi0MY1Gt6Fss5rNimSBVmvw97ptFUYkHen0\nKlnHssQLGxv8iqgN1AoFf7/cWdoJM2mSGXJkpy+VRhhOIV1AKp7Ckbpa0goC/P3WfphJUyvLIh53\nmy7SJR0/wCcy/ExGfG1BWTqRGb6qyZO0dlusIAMAXyVpBjF83dVtuy3+LSfDp/SjmZgQORvDz/+R\nxUcAgCzpyGFoa/iLiyIjbOj5r86tdoP2j5WNBfiMsVcwxrYzxvqMsfOG/va3jLEdjLEHGWN/MN4w\nI1gQwyf20wlqTyCdnsrwfSUdgAb4PpslUxn+5GQA4Jd34pTJU8hZCr4MH1Dr+D6SDmMMq3OrcbB2\nUHnfoBbJ2+e2Y9PMJvL4ZS989/AxGH4ulUM6nlYyfMb8G6hxzsdj+KomT9JCVrdAdElHpmTq5OAD\nQ3n46XRkhk/tpxPESR4pCcA/dYrG8OX5kTT8qamB+A8ArM7+lgM+gPsAvBzAz7y/ZIxtBvDHAM4E\n8HwAX2CM0aqUlstCGD6grrYNcnqZlpZJZEZP8jFfSQegOb0f4BMZflBs9dHSo2Q5BxCAH48P5SID\nasAfqjSUtia3huT0QUR8+9x2nLnqTOX50jzb0gqjAD7nYkIeAnzGmFbx1bDvWC0LzW6TXKENjNQO\njgX41BbJQZKOrLLVaasAeACfMcHyIzJ8qiQoecYwLu9Y3IFCukCuspXnj6xuVRr+UB8daatzq3Gk\nfuQx7Zg5FuBzzu/nnD/o86eXAPg3znmLc/4ogB0Azh/nXtqmcvqoy1rNoqtlZ/hOi2RVap0f4HPO\nsbO0E0+aoKelyaaFLlkJepsGb+TL8AFoMfxhwC83yzhQPYAzZ/UA3/SmjKua7QPis7XbI4APOMVX\nRMAfZvi6OfiAjxSv6r0sT5LHeoyq4YeRHWAMORMQkiaV4Q+cSG+gFsbwnzz1ZO3VrcvwTVNINVSG\nP2Src6vR5/3HNHC7Uhr+WgB7PT/vc343YoyxNzPGtjDGtsypHEHHAtIyx81U2GftI8s5gI/TT04K\nyjyGpNPjPWWb1clJUR/irRGZs+dQ79S1Gf7Aypoi6dRqAlB9AH9Nbg0OVtWA75els/3IdgDQAvwR\nhiy/iNCG9c4KxA/ws/R+OssB+CPjpzTwCgD8dCKNbDI7lqQzY86QduoCAgCfwvAtS5w0FL+iMvwg\nwN+xuIMcsPWe7wK+rCuhAH4AwwfwmAZulYDPGPsRY+w+n38vCTvN53e+lJRzfjXn/DzO+Xmzs7RA\nIsmC0jLHlHT2V/drp6UBHpYZiwmnVwH+0PaG0qjtFfxwWTdDB/ABfIqO6VNlK21Nfg0WGgto98I3\nEpcM37uQ2T7nAL6GpOPuZyuN0kDtsPNCLjPD313ZDYAe/+l0xEJjALfXrgX27w8/MQDwAVodSpCk\ns8/ap110BURg+EN9dKS5vaQUvu/not1+F7vKu7Rz8AEf/6dk6QQwfACPqY6vrP7gnP+3CNfdB8Ar\n9J0E4ECE60Q3GSk3B0vAqUFbP8BvdVs4Uj+ixfDlknyArKxaFVnD97ZX2IANgad7AX/NGvH/ywr4\nYQzfp4+OtDU5MZhDtUNYX1wfeIlCYak7hvwKtx/ZjmwyG3qe31BmvBmclJ74EvBXjzJxnY6Zw3P6\nnfvuRD6Vx2lTpynPBwLCUCedBPzXf4WfGAL406Y6LTkoYWGvtRcbisE+N2w+Hb7pDH8oYAsskTWV\nJOIH+Hsre9Htd7UYfqUiSP3A+CmAHyLpAI8t4K+UpHMdgD9mjKUZY08CcBqAX6zQvfxtzx5g3bqR\nZaG7EUQEhi+158il5dJmZ8eSdAA6y/Hisiy6Onni5PB7e2wE8GW6GYXh+wF+XgC+Stbx66ezfW47\nNs9uRozR3XYkfjYuw8/Oot6pK9N6/Rj+HfvuwAUnXUDusuqrSp50knj2YZLUmAw/FhM95kYAv6Lf\nVgHwYfiVili6BFkAw1+VXYVELOHGEoJM+qvX93cs7gBAz9ABxGMeUZZUHTObTbE08pF0ZMPC31rA\nZ4y9jDG2D8CFAK5njN0MAJzz7QC+DeA3AG4C8A7O+dENTe/eDWzwZyPThrqBmt+uRbItATVoBYxs\nbSlM1V5B9iT2cXrJElSBzyBJZ3VuNbnxFeAD+PLiYQw/TNLxMPww8yPiuhk6wBiAH4/7jp+aiz/c\nI6/WrmHb4W248KQLqUP3VyXXOQvnMFlHTlg+oKNbeCit3q6j1CyRUzKBEA0fCC88DGD48Vgca/Nr\nscfaE3rfZFKM38tJZEqmjqRTqYwUW6s1/IAqW0Ck9WaT2d9ewOecf5dzfhLnPM05P4Fz/geev32U\nc34q5/x0zvmN4w9V0/bsAdb7L/11dEwvy7nl0VsQYzGcd+J5/if52MDmJ9JUko7sTesD+HJJvbu8\nO/S+fsk0Mgdfx3wBX7WsDZN0JMNXTFjDresX7AUcqh3SCtjKxoy+gK+SdFatGlkdAvRq22GGf/f+\nu9HnfS3AD5R0AGBfCMvdtUt8Th/QobZIHq7UfnBBJONtmNCXdEYYPhAu6wQwfECkhMr00DAbdtFH\nFh9BOp7GifkTledKG+ijE3ThYQsBfOCxL746NittOx3BgAIAn6Jj+kk6N+64EResvYC8PRoQIOms\nWiWceriMV1pAHx0AyKaymDam3QBgkAUxfJ2UzJHNT7wXj8jwV2VXgYGRJR35KNyArQbgy2EMAL5q\nh3TAt+hKmk4/HdnlFwBu33s7AOCZJz1TOW5pvsoMBfAffRR40pNGCn8AesfMyckl7AKA7z/4fTAw\nPPdJzyWOXjziVMrp5S9NMvwwwhPA8AFgfXG9WwAWZsOFhztKO3DK5ClacmC5PAbZ8VldAccBf2Xs\nwAHBkMMkHWLxiQT8w7XDuPvA3XjBaS/QGoqvpKPqKeIb7VqyDRMblIA/rOG3ui3ss/ZpMfx6XQRO\nfZ1eFbRNJEYypAAgEUtgNjurZPgjgH9EP0PHt6UJVdIJAnyH4asCh7mcyEyVUvUd++7AGTNnuDEY\nivky/LWOnLg3BPQk4PvYtDGNbr+rTOsdTqa59sFrceG6C8kb5wAh8SsgOsMvCIbf5z67s3jMj+Hr\nyDlyGL4M37YFqfQz6XTHGf5RtD2OxhfE8AkavmzRK53m5kduBgBc+uRLtYYSKOkAwTp+QOGJtA3F\nDUpJJ5EQp0tcvvbBa7UlBd+0NCC4b4M0WXQVUOCyJreGDPgSl7fPbUc+ldfSkH3fPflMwwJvhw6p\nGT6xRXK9Lgre7tx3p9azBwIYfiYjQDOI4XMeCvjUatvZ2SVM3lPZg18d+hVecnpYJvao+QK+iuF3\nuwJQAxj+usI6dPodZT8mL+CXm2U8tPAQOTtKWqCkAwT7z3FJ5zGw3Q4YBjF8R9JRsQSv1H7jjhtx\nQvYEPH3N07WGEhi0BYKdPkTSAcSydndlt1a17ZVbrsTJEyfj90/9feLIffroSFMxfJ/GaV5bk1cX\nX/lJOptnN5OrJIEAhp9OCzTbHTBhch7K8CcyE0jEElotkh9efBgLjQU8a92zyGMHAruDCFknCPDn\n5wVgnnyy75/dnv6K8c/MLLnndQ9eBwDLA/jyywhi+IrVrUzJ3VMJD9x6Af/LW7+MVq+F1zz1NZRh\nu+Yr6agaqBEknVKzhFY3QM5dYTs2AV8y/HX+bHDamEaf95UVezKZptvv4uYdN+PS0y7V0gABxbI2\niOGHZFkAguHbHVsZh5C4fP/c/fjprp/iLee+hZwSCIQA/uSk+GBB7Ql8WiN7jdJPxxtb3V3ejTv3\n3Ylz15xLHLmwgC61wKZNwG9+43+STBn0ycEHRD+dGXNGaxOUO/beAQDaDD+gWDwc8B8VqbdBDF9K\nerJzZJB5syevffBanD59Ok6fOZ06dAABvp9ICN8IIjsBfXSkyT4+qsCtBPxuv4vP/eJz+J0Nv4Nz\n1pxDHnu/L3wvkOEHAf7CwlKakI/JLDtKx9iVsGMX8GdmRoqupEmWIPPSg0wC/l377kKpWcILnqyn\n3/f74qXVlnR+/WvxYmzc6PtnmSlBCdyWSsBVW65CMpbE65/+ep3hhwO+94BhUzH83Bocrh8OXWFl\nMuIRWBbw3h++FwwM73v2+zRGHwL4mzcLwPdbIYXk4EujVNt6Af+WXbegmC5i0+wm4siXzgUCGH6Q\nhq8A/FOnTgUDc7Nugkxykp37LPx010+12T0QWCw+qBcNm1w5hgRtATrD//ft/4E9lT34y2f+JXXY\nAMSz7/cjSjo+nTKlPdbFV8cm4Ifk4ANwX7z75+8PvYwE/G/8+huIszied+rztIYRyNAKBZG6EAb4\nZ5wxlN6wZDqpmQuLfXzt3q/hjzb/EVZlV+kMP1zSAcKXtSEMf3VuNbr9bmjgU1Y4bt+7B9+5/zt4\n/8Xv16qwlcNIJn2e/+bNYuyHfXqaUACf0DFT3vOm7T/H1+79Gv74KX+svTqU2+oaw61r1q0TH853\nS7NwwM8kMtgwsQEPLTwUem8ptf/7L3+Kbr+Ll5yhD/iyJY7vxYMY/nYRnMcZZ/j+eTIzCTNpKjN1\nJibEfH7FT6/GKZOn4EUbX6Qx8jF9P2BlDhwH/JWxkBx8QBRfxFkcD8w/EHqZVauAI3N9XPmLq/CG\np7/BbWtAtZFOmdIYC8/F37YNOOuswOvqMPy9h6uotCp423lvow7bNSXDD9LxAzplSqNW2+YLHD99\n6Fc4dfJUvPdZ76UMecBk0dUI2dq8WfzXT9ahMnzirlf/8JPP4fy15+PTz/80cdRLtrg41KlUmkzN\n9Cu+evRRAag+VbbSNk5vVAK+ZPgfvelqbJ7djAvWXqAxcmGRGP7WrWKGO91fPmKMiUwdAuADwJad\nD+NdF7xLS8oEfBqnSfMr4/VaQB8daccBf7mNc8HwQwA/FU/h1KlTlQz/fvu/0O/F8LInvQFf+MMv\naA/Ft/BEWlB7hUpFTFhPfWrgdaeNaZhJU8nwH6zfiWoljtee/Vo8e/2zNUa+NBRAk+X0euL3CkkH\nCC++4pyjin2wrD4+8/zPkPcf8Frgu7fJkVbGAXwFw+8nRbTZ5KvwvVd9L9L4Dx4ETvSrEwrLxd+1\nKzBgK+306dPx0MJDoUH/vZ2tAICJ/mn4zz/9T23ABEIAP4zhb90KnH220PMCbH1xvVLS2df+NQDg\ntOz5eMPT30AdsmuBGWonnCBW3g8FTJgBfXSkyVX2ccBfLiuVxFo4RNIBgE0zm3D/XDDgbzu8Dd/b\ndzUA4LLzvhDZ4YEAshXUXuHXwlHDAJ8xJlIzQxj+FbdfgdvnfgB0crjq0n/Sym6RJjc/GdGQZTD8\nQR8dWM4SYzL8y2+/HIv9XTjZeCr+cOMf6gzbtYB9KEQ3uWIRuN/n+z98WFTYKpbl5WYZtXZwP5uP\n3/1BAMBbznqP+3l17cCBpcZ3AyYB30/HD0nJlLZxeiOq7Wog6FgtC+/+uchoecfmy7SqU6XJbXVD\nGf7whNPvA7/6FXBOeHBV5uIH2W17bsP/2SLiPZ949peQTfkHUMNspBe+tEwGOO884Oc/9z9RIemk\n4ilMG9PHAX/ZTJGDL23TzCbsWNyBTm+0gIJzjvf+8L3ITggRvrSQHDmGYoGSDqAG/BBJBwhnOUfq\nR/CBWz6As04WwGxVom02JutfRuaKDRvEvx//ePQkyZpDnr+qn84PHvoB3vej92HNdA4zcb1WEF4L\nBHzGlgK3w3bokACkePAze9rqpwEAth7c6vv36x68Dv++4ysAgOkxxq/N8Pt9sbolAD6AQFnn8tsv\nxwIeAmMcnZp/8FRlsjtIIMOXfS+8tnOn+J0K8IvrcKh2yLfFdp/38abvvwkzU84KoaUnw0oLlHQA\n4OKLgV/+0j+GopB0ACcXv34c8JfHFDn40s6YOQOdfsdtGey1Gx6+AT/a+SO84/deAUDd2DLIlJKO\n37J22zbhZSeFdyUMY/ifu+tzaHVb+NPzRaBKtRthkPn20QEEYD73ucAttwgJx2vXXy/A8rnBJfhG\n0kAxXfSVdDjneP9P3o9Ns5tw0ZPPgmXpr0ykBQI+EAz4ITn40p6x9hkAgF/sH20Au2Av4M3ffzOe\nuv4UmCbHgYhNwTkXgO/L8A1DfLBhwD9wQORRjgH4B6sHccUdV+BVZ70CU1NM2cU7yJS+D4zq+Fud\nCVQB+OuL68HB3f2lvXbTjptw//z9eM8lIiNN1ck4yAIlHQB49rPFhHX33YO//81vRD/vU8M7cj6W\nxVfHHuBTGX5Apk6n18F7f/hebJzeiHde8koA4wN+oKRj26M9aGXAViHBbJjYgHl7HvX24PnVVhX/\n9+7/i5dtehnOXC/o4bIDPiAAvVwWS3Cv3XCDeCECTxQWtNXh7Xtvx7bD2/DuC96NyYlEaI+zMONc\nsbretEl8scNdGwmAvyq7CidPnOwL+J++89OYs+fwLy/7GtatY6EdEMJscVFgty/DB/xz8XftEv9V\naPjri+uRjqd9Af/D//VhtHttfPQ5HyXtVRJkJMAffjhbt4q0qjPD22fIamu/wO3lt1+Otfm1eM0z\nhAwYFfAD41cAcNFF4r/Dss53viP++5LwjKYTciccB/xls927l8rPQ+yMGZH2NZyp881ffxMPLjyI\nTzzvE1i9KgnGogN+qKQjdXAvYHIuJJ0Q/V6aTM0clnWu/uXVKDfLeN9F71Mm0/T7S1lwfhYK+M95\njvivV9bZu1dMWH+o1tyDqm2v3HIlCukCXn3WqwM3MpcWVmhs26I3XSjDB0Z1/MOHA4uuvHb+2vNH\nAL/X7+Gf7/lnPP/Jz8fZq8/GunXhLW/CTK4MtABfkZIpLcZiOG36tJFc/EcWH8GXt34Zbz33rTh1\n6tSVA/wLLxQ1Mt/4xuDvt24VZCcgHVlaUC7+1oNbccuuW/DuZ74b05NChg0CfM4FQQ/yoXJZLKTS\naZ8/Tk4CT3kKcOutg7//zneAZz0r5EsTdnLxZOyp7IHVishmxrBjD/BlSqaCIRfSBZyYP3GE4X9p\n65ewcXojXrTxRUgkBGCEAf6uXULZ8DMJVr4M/8UvFo5zxRVLv9u9W7wpFMD3Sc1s99r41J2fwnOe\n9Bycv/Z8JeBffbXw23vu8f97KOCvXi1O9gL+jU4X7BeoC9Q2zWzCPYfugd1Z0kHn6nO45jfX4LVn\nvxbZVNbdb3xYNQIE1s3MANdd5399RQ8r/9TM224T38HT1e0zzj/xfOyu7Mbh2lIu/82P3Iz91f1u\nVshyAL6vpBN0cQn4CjkT8E/NvPqXIknhby/+WwDqzam2bAHe/nb/gutQwJ+YAP7kT4BvfnOJSnMu\nAF8h5wDB1bZX3HEF8qk83nTOm0Z6SQ3b9dcD558PfPe7/n8P9X1ArGJvv33JOXfsAO69F/ijP1KO\n/9LTLnWr94+2HVuAz7l48Ao5R9pwps79c/fjtr234Y1Pf6Ob1RK2V8n27cAFFwDPe54/E927V2S4\n+DpOLge8853AtdcCDzirDGLAFvAvvvrWfd/C/up+/PWz/hpAeLo858DnPy/+X65Eh03p9M99rmA5\nss3z9dcLsJFgGmKv2PwK1Dt13PDwDe7vvvKrr6Dda+Ot570VQHhjyx/8QMge73mP/+ZJgVW20tat\nE1+OBHzOgb/9W4Gwb3mLcvznrz0fAHD3gSUd98tbv4xZcxYv3PhC9xYHD/o3Vnzb24A3vAH49rf9\nWVcrVK4AABYDSURBVOhBZ/ETSBbXrxdo7J2wHn1UnJBRp4BunNqIR0qPoNsXaN3utfHVe7+KF53+\nIjcrJ4zhHzkCvPSlwJVXivjlsIUCPiAegG0D//Iv4ue9e8WXRgB8M2liypgaYPh7Knvwrfu+hTed\n8yYUM8JpwzoZf/Wr4r/f/Kb/330bp3nt4ovFh9y2TfwsX6KXv1w5/gtPuhAz5gyueyiAraygHVuA\n/5GPCIkkJGDotU0zm/DA/ANuPvI//eqfkIgl8Gdn/5l7TBDg33cfcMklAuh7PeCOO0aP2bFDxG8C\nFxvvfKdYM15+ufhZOs9TnqIc+4n5ExFncdfpOef4zF2fwaaZTW6DNL9NUKTdfrv4DOk08L3v+d+D\nBPiNhvjwrRbwox8JOYeQAvo7G34Hq3Or8W/3/RsAAThXbrkSv3fy72HzrJgwwraf/eEPBa498gjw\nxS+O/l0J+LGYqObctk2A/U03CU327/4usCWH185Zcw5iLObKOodrh/H9h76PPzv7z5CKC0li3Tpx\n6eH6qL17gauuAr72NeBVrxIKx7ApGf5rXytiDS99qfiC775bLHc20do3nD5zuruxNyAyi47Uj+BN\n57zJPWZ2VjzH/lAHjF4PePWrl9j/T386en1FhwTg3HOBZzxDzBiS3QMkwAeErLOjtMP9+bN3fRYA\n8K5nvsv9XVBT11IJ+P73he9ff70/ofBtnOa1Zzt1LVLW+c53RLomYXUVj8Xxwo0vxPUPXe9mCf7D\nz/8B12y/RnnuuHbsAP5nPwt86EPAn/858Nd/TTrljJkzUG1XcaB6AO1eG1+792t48ekvHuj5HQT4\nL3+5iC/dfrtISvnZz0aPeeQR4MlhLbhXrQJe/3rBct7yFuBjHxMVhoG0aMnisThOmTwFN+y4Aa1u\nC3fsuwO/PPhL/MUFf+GuTlIpgV1+DP+LXxS3+eAHBfDv2DH498DNT7z2u78rPvz//t/Au94lGBtB\nzpHjf8XmV+D6h69HtVXFF+7+AnZXdrurEyAY8LtdoST9j/8hQgl///ejrU2UgA8IlnbLLeLlfe97\ngVNOEbSbYNlUFk9Z9RQX8P9127+i2+8OFPnIMM2w8iLJwa23Ah/4gFjgHRqK4R08KBjmSFsFaSee\nCFxzjWD1l14q2EehIACUYDJT58F5oeN/aeuXsK6wDn9wqrtpHWZmBLgP+89HPyqe/xe+IBZzfoD/\n8MNiTg2NH7/1rSKG8ra3Ae97n/AlgpwJiDblP9r5I9y651ZUmhVc/cur8cozXznQfiOI4X/722JV\n+PGPiy1o/WRB3174Xlu/Xvy76irg/e8XE+5//++ksQPAize+GKVmCbftvQ33HLoHf3fL3+Enj/6E\nfH5k45w/bv6de+65PJL9+MecA5y//OWcdzr003b+mOMy8Gu2X8Ov3nI1x2XgNz5848Ax73wn5xMT\ng+ft3y9u9+lPi5+f8QzOL7548Jhul/NUivO/+ivFIB55hPNEgvN0mvM//VPO77uPPP7/+M1/cFwG\n/o7r38Ffec0r+cQ/TvBaqzZwzNq1nL/+9YPnzc+L27397Zzv2iU+yyc+MXhMtSp+/7GPKQbxqleJ\nDwpwvno15/U6efy37bmN4zLwz975WT75j5P89//193m/33f/ftNN4rK33TZ43q23it9fcw3nW7aI\n///ABwaP+fznxe8PHgwZQKvF+ZVXcn7iieLgr3+dPHbOOX/jtW/kk/84yW/bcxsv/p8if/ZXnj3w\n99/8Rlz2G98YPO/d7+Y8kxG3v/12ccz3vjd4zMtfzvmmTYRByA/61KdyfuAAeexz9TmOy8D/8qa/\n5Fv2b+HsMsY/dMuHBo75+tfFpR94YPDcdes4f8ELxP+//e2c53Kjr90rX8n5qacqBlGvcz49zTlj\nnD/zmZx/85vk8ddaNb7+U+v5mZ8/k//Dz/6B4zLwLfu3DBzz4hdzfvbZo+dedBHnmzdz3uuJ9+NF\nLxo9ZuNG4dqh9rGPLflOMineZaJVW1We/kiav+vGd/FnfvmZfPbjs3zRXiSfP2wAtnACxj7mIO/9\nFxnwOx3OP/lJzptNrdMOVg9yXAb33/pPrefdXnfgmL//e/GUWq2l3333u+J3t98ufn7PewSANhpL\nx+zeLY754hcJA9m+XaBwBPtfN/8vjsvA2WWM/9UPR2eXM8/k/GUvG/zdJz8pxnbvveLnpz+d82c9\na/CYffvEMVddRRxIp6M12XLOea/f4+s/tZ4n/j7BYx+O8W2Htg38fetWMYZvf3vwvA9+kPNYjPOF\nBfHz857H+VlnDR7zkY+Mfm+BZttiFvFMNhSTJCH1kRQ/7bOn8V2lXQN/l5PmP/7j4HkXXLBEEBoN\ngRV/8zeDx1x4IefPfS5hEP0+5z/5CeeVitbY+/0+P/nTJ7u+H/twjO8u7x445uabxfh//vOl3x04\nIH73yU+Kn7/1LfHzXXcNXv/ss5cmhVDbu1cxKwfbdQ9c5479kq9e8v/bO/sgK8vrgP8ObGRRxrBU\n2SgfyjYorCgLbAUR3DWSBAzfxY/GAaZNxjHDTFNlxuowybSdiTONnbbpGJMxRmONYpWPwGha1w/A\njBG2ILsUi6uLiYCiIospCm6EPf3jvI/3670fu8u973v3Pr+Zd+59n/vs7rnPvu95z3Oec86T8fmK\nFaoXXZTa1tmZ+j+54w4b/640XTtypOqttxYoyMmTmb+gAK5/7Hqt+ocq5e/QR9oe6fXPJ1Oowh8Y\nLp2qKrj99iwxVNn50rAvsfbP13LfvPt4dMmjoTVDwvYqaW21P9lgCZdcc425sJPzMJyLJE8OhlFf\nn8f3kJ17rruHWWNnMUgGserPVmV8Hrb97Lp15m50s+clS8zNkOxWyBmHHEZVVc76J2EMkkHcWH8j\np3pO8e0p3+by2tTF6okTbZbf3p76cy0t5v51ETgzZ9oCevKm4UeP2rp4ngg/Y+hQi63uZfkJtz/t\nhPMm8Ju//E3GBt/DhplbINml8+mn5q52fvvqaisds2NH6u/OWlYhHZGEO6cXiAjtt7Xz/PLn+eGc\nH/LgggczqpGG7cTprvErbc2apiZ7TXbr9PRYqZks9c9SGT26oDDYMBZcuoAlE5bQoz2sviqzuF6Y\nS+fxx23Ibgn2QrnpJltUT1/HyuvSSaa6OmcpkWwsvGQhp3pO0XRRE8uvWN7rn+8ThTwVSnX02cIv\nIhs2mEXw6quJtuuuU506NXH+4YfW5wc/SLQ98IC1/T7V6CsKx7uPZ1jHjgULUqe13d02G1m9OtG2\nZ0/mbMS5Gn796yIJHbC/a78ufmKxvv/x+6GfX3aZ6vz5ifOuLrPuv/e9RNszz5isW7cm2pYvz7Tu\nikFLZ4seO3ks6+eXX26uBYdzR23cmGhbtcrcIqeCyWVPj3nJ7ryzSEIXyIEDmdfFmjWqgweneu4m\nTlSdNy9x7tyEBc8O+0HXiS596rWnUlyBju9/37xFp08n2pqazAXr6OlRHTs2dRZ88qTJf889xZNb\nVfXoiaO65Ikl2vFhR79/F6Ww8EXkBhF5TUR6RKQxqf1iETkpIm3B8dN+P5kiIn2vkp4es3KchQNm\nnNfXpybedXbaom6eCglnhGFnDcuwjh3pFv7u3TYbSY4MmTTJ5EzPoYLE9y8WdTV1bLxpY9Za/Q0N\nqXkCL75o/4OvJ9YWP/9fJFvJOcsqnEG++qdfzVk2Oz1c3i3YJo//jBk2O3ERli7LtiALv4iEVUBo\nbbWo4eRApuZmu/ZdPL6rqZelpP0ZpWZoDcvql4UWB3Q18d1s9bPPTH6XKAtm7Tc32wK6BklYvZ7d\n9pERQ0ew4aYNny+gl4L+unT2AkuBkBgV9qtqQ3Dc1s+/ExnpCv+NNyxqZHpaefDZsy1vx+Vh7N9v\nQR85anCVhHSFH6ZwRGxqvm1b4qLfutVcEgUGTRSNyZMtycpF3Tz7rHkvkh+4551nrrPWpMTXUin8\nfIwZk6j2ATb+dXWp1RvcteQeWHmzbEtEdbVdA86l44yd9Gu/udkeWC6y0in8glw6RSS9indbm0UR\nz0zbWnjWLPuOb75p5y4HIk8NtLKkXwpfVfepau690sqcdIXvlEqywgHz4x8/nvA3uxj8qEnffvaV\nVyyaLF2ZNDVZVQFX5nvLFvtOX+hbodAzhlsnaW+3h1FLi4Vipst15ZXRWPj5GDPGZDlxwuR/5ZXM\nuPsvf9mUy/btdu4UTtQWPqSWru/sNOWZfu07P/5zz9nr66/bQzlPSaKi4/7+/mD73pdfttdkCx8y\nQ+pbWsL7DQSKuWg7TkR2i8g2EZmdrZOI3CoiO0Vk55G+Fu4oIum7Eba2Wvx6uvVy7bVmKW/ebDd2\n3hj8EuGm5e6iD1M4YModLJ/g8GG7aa+9tjQy5mLyZHttbzcL7O234Wtfy+w3fbrNBJx1HCeFDybb\ngQM2tunjL5L6wIqLhQ+p2bbZjJ3aWmtzC58dHXZ/9GELhjNKc7MlUz8V5DP99reWF5A+rhMm2LXi\nFP7mzVZdw/3vBhJ5Fb6IPC8ie0OOXCXhDgNjVXUKcAfwuIiEhhGo6gOq2qiqjefnKXgWBW43wmSF\n39iY6aq54AK7wNautb4ffxwPC3/xYrOG77/fMj4PHgxX+JdcYjfutm2JiIs4KPyRI21s29oSlley\n/97h3AytrQVtulUyXJWPgwctqxPCLccZMyzS6PjxeFn4ybsRtraaAg1L5l261GrrHDyYUPhRc/bZ\nVrhy3TpbE3n55Ux3Dtg9fvXVpvCPHDGjaEHvtsAtG/IqfFWdo6qTQo5NOX6mW1WPBu93AfuB0q1M\nnGFqa02Jd3eb4km3cBzf/Ka5RJ580s7jYOFfeKGFnj30kFUPgHCFL2JW/rZttjA6fHjCnRI1DQ1m\n4T/7rD1E60L2FGlosAfbjh32YFCN3qUACSvxrbfg3ntNsbtZSzIzZ5rMv/ylWfhf/GJBFR6KTrqF\nH2bsgIX2gsl/6FA8FD5YjbauLvjZz2xcs7lpZs2yGeTDD9taxcKFpZWzZBQSypPvALYCjUnn5wOD\ng/d1wDvAiHy/J45hmaoWcjZ2rIXXger69eH9urosnG7UKA3NUIwKl416/vkWkpktGem++6xfTU1q\nKGHU3HWXJcecc47qd76TvV9jo+q4cZbFesUVfcqFOeN8+qmN6aWX2uvTT4f3O33aEsiqqy2MtqAs\n2xKwerWFYa5YkT9zvL5etbZWP8+CjgPd3XY9jxhhcu3eHd7PhSHX1FjybC9z8CKHEoVlLhGRQ8BV\nwDMi4up9XgPsEZF2YB1wm6p29edvRcno0eZ/3b7dSq5km+7V1FgpmXfeKaCOSAmZNs2iiI4csffZ\nkpHc4tuxY/Fw5zgaGiyk7pNPwv33junTrbRMXZ3VcetDLswZZ8gQc0t1dFhdsGylhgYNspJK555r\ns5k4uHMAbrjBrN8XgzIvc+dm77t0aWIP+LhY+GedZd+hq8sijrIVop02zaKSjh2D+fOjX38oGoU8\nFUp1xNXCf+89S+oppHLAk0+apVCKpJ/esH69yZWccJXO6dMJS6itrXSy5WPfPpNp8GDVjz7K3m/X\nLtVly/qcqV80pk0z+TdsyN/XlTNYvrz4cvWWfFbvrl0mu4hVq4gLW7aYXHPm5O7X1JR7FhZnKNDC\n710ufIVSW1u4P3j+fLMk4uC/T2bRIiv3vnJl9j6DBpll/9JLBZXkLxnjx1v1g2nTcifDTJ2aiMiI\nEw0NZjHm2fkOsBnMxo22iB438lm9U6ZYdWCRHFU+I2D2bPPd33hj7n5z59rCudvMbSAi6jJtYkBj\nY6Pu3LkzajH6zaZNFr9cjnG8775rIY1xUvhg5ZzHjy/Pm7Gnx/IgCqrrU+Zs2mQRaq5WTTlx+rS5\nDXtZligWiMguVW3M288rfI/H4ylvClX4A6Napsfj8Xjy4hW+x+PxVAhe4Xs8Hk+F4BW+x+PxVAhe\n4Xs8Hk+F4BW+x+PxVAhe4Xs8Hk+F4BW+x+PxVAixSrwSkSPA2/34FecBH+btFU+87NHgZY+GcpYd\n4if/Raqad0ORWCn8/iIiOwvJNosjXvZo8LJHQznLDuUrv3fpeDweT4XgFb7H4/FUCANN4T8QtQD9\nwMseDV72aChn2aFM5R9QPnyPx+PxZGegWfgej8fjyYJX+B6Px1MhDAiFLyJzRaRDRDpF5K6o5cmF\niIwRkS0isk9EXhOR7wbtI0TkORF5M3iNwRbc4YjIYBHZLSJPB+fjRGRHIPt/iEhs93YSkeEisk5E\nXg/+B1eVy9iLyO3BNbNXRNaKSHVcx15EHhKRD0Rkb1Jb6DiL8W/B/btHRKZGJ3lW2e8Nrpk9IrJR\nRIYnfXZ3IHuHiHw9GqkLo+wVvogMBn4MzAPqgb8QkfpopcrJKWC1qk4EZgCrAnnvAl5Q1fHAC8F5\nXPkusC/p/B+BfwlkPwZ8KxKpCuNHwH+p6gRgMvY9Yj/2IjIK+GugUVUnAYOBm4nv2P8CmJvWlm2c\n5wHjg+NW4CclkjEbvyBT9ueASap6BfAGcDdAcO/eDFwW/Mz9gU6KJWWv8IErgU5VfUtV/wg8ARSw\nXXQ0qOphVX01eH8cUzijMJkfCbo9AiyORsLciMho4BvAg8G5AF8B1gVd4iz7ucA1wM8BVPWPqvoR\nZTL2QBUwVESqgLOBw8R07FX1JaArrTnbOC8C/l2N7cBwEbmgNJJmEia7qrao6qngdDswOni/CHhC\nVbtV9XdAJ6aTYslAUPijgINJ54eCttgjIhcDU4AdQK2qHgZ7KAAjo5MsJ/8K3An0BOd/AnyUdDPE\nefzrgCPAw4FL6kEROYcyGHtVfQf4J+AApuj/AOyifMYeso9zud3DfwX8Z/C+rGQfCApfQtpiH2sq\nIsOA9cDfqOr/RS1PIYjIfOADVd2V3BzSNa7jXwVMBX6iqlOAT4ih+yaMwN+9CBgHXAicg7lC0onr\n2OeibK4hEVmDuWUfc00h3WIpOwwMhX8IGJN0Php4NyJZCkJEvoAp+8dUdUPQ/L6bxgavH0QlXw6u\nBhaKyO8x19lXMIt/eOBmgHiP/yHgkKruCM7XYQ+Achj7OcDvVPWIqn4GbABmUj5jD9nHuSzuYRFZ\nCcwHbtFEAlNZyO4YCAr/v4HxQbTCWdgCyuaIZcpK4PP+ObBPVf856aPNwMrg/UpgU6lly4eq3q2q\no1X1YmycX1TVW4AtwLKgWyxlB1DV94CDInJp0HQd8L+UwdhjrpwZInJ2cA052cti7AOyjfNmYEUQ\nrTMD+INz/cQFEZkL/C2wUFVPJH20GbhZRIaIyDhs4bk1ChkLQlXL/gCux1bO9wNropYnj6yzsCnf\nHqAtOK7HfOEvAG8GryOiljXP92gGng7e12EXeSfwFDAkavlyyN0A7AzG/1dATbmMPfD3wOvAXuBR\nYEhcxx5Yi601fIZZwd/KNs6YW+THwf37P1gkUtxk78R89e6e/WlS/zWB7B3AvKjHPtfhSyt4PB5P\nhTAQXDoej8fjKQCv8D0ej6dC8Arf4/F4KgSv8D0ej6dC8Arf4/F4KgSv8D0ej6dC8Arf4/F4KoT/\nB/J/7SfRV0+bAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1c2b5c82b0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "x = np.linspace(0, 40, 130)\n",
    "x1 = 2 * np.sin(x)\n",
    "x2 = 2 * np.cos(x)\n",
    "\n",
    "y1 = 1.6*x1**4 - 2*x2 - 10\n",
    "y2 = 1.2*x2**2*x1 + 6*x2 - 6*x1\n",
    "y3 = 2*x1**3 + 2*x2**3 - x1*x2\n",
    "\n",
    "plt.title(\"Ground truth for 3 input signals\")\n",
    "l1, = plt.plot(y1, 'r', label = 'signal 1')\n",
    "l2, = plt.plot(y2, 'g', label = 'signal 2')\n",
    "l3, = plt.plot(y3, 'b', label = 'signal 3')\n",
    "\n",
    "plt.legend(handles = [l1, l2, l3], loc = 'upper right')\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Both input and output sequences"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 274,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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r61R4vdjsdvq3sbEbjsJOqseCqNc0bEoxrgNBxKXr7He5GJ6QQE+rlf0uF7pI\nu05bzX4/jZrGxORkrN+AhdTll16KiLDb6YxgxME2CYfPeG+I3U66zUaG3d4h86zyevGJMMBup9nv\nx6oUKTGasCDQP/0iDDLa1aQU1V4vJqXo1SIcsVmpCHoLXC6SzGb6tjOOlVJ4dZ08w9GqR1YWEwz/\ni28LMaktpdTrwFygt1KqFHgAmKuUygEEKAR+Gou82oJJKf4SZTe+JX5TUEC5x4M2Zw5mpRi8di2n\n9ewZM4b/QlkZT5eW8uqYMczpwPrkqZISfltYSN2sWSSazSyurMREQHJuC+fu3MnGpibuGjyYi/v0\niSmzB1iYn8+l6el0azGQfLqO2Zicgni4sBCXrvO7YcMYkZjI7mnTyGzHPNOiFD8dMIBRSUlMSU1l\n34wZMaUd4KDLhUUpGvx+elgs9DGY4bCEBFJblCknJSUkRTt1nTKvlx4WC4ltMB6H388el4tRiYnU\n+nw0u1z0s9nafP9IMDwxMWLvp97nQxMhzWqNYJoJJhOjEhNDpq29rdYO94w8hvVPf4Mp6YZ0Hct9\nIKUU48MmKxFhn8tFT4slQqgxK8WwhITQiqNPJwSeRmPCSjGb6ddJAakr8Ivg1nW2GZvm6TYbjX4/\ntZpGD4slou87/X68uk53iwWlFH5jhdUeBtrteHWdRk3Dpeukms3fuudrTBi+iFwW5fZfY5F2V+HV\ndWztdODbBg7koj59QlLc5ilTSInhgE23WpmcksJV/fpR4/NxVV4efxwxgv0uFysbGvhlmO3/cd26\n8ashQ0IM4+WKCny63ibDD1qGLBw8mAcyM2nQNO7Jz+ey9HSyYyQpFMyciVvXeaGsjIkpKSyprMTh\n97O8vp6nR4zgJ2GbrEUeDw5DQreZTB2aZPaz23li+HBGfPUVvxo8mJsHDowJzUGIYfFkVopEs5kE\nkwm7yUSycS8agky0p8VCj5SUdtU6FpOJ/jYbCSYTVpOJJr+fXU4nkzr4rqtw6zqHvF4G2O3UaBpu\nXSctioQZPim3lECjIc1qpdrnC3mBCwFJO1Z9p0HTqPR6GZqQEFpBKKVQBCablvSH0xxktokmU5tC\nzCC7nUKDqSaZTOS73XQ3m+kdI+Y/JCEBEaHM4wlNRAPtdgbb7a1oqvH5qPL5mGyYUo/opKe8zWSK\nGb1Hgu/VASj35ufzQnk5tSec0Ka1ztTUVP5v/368us5/6+s5Ny2NM9PSYkbDhenpXJiezj6nk/er\nq1leX8/Gpia+rK/nhfJybuzfPyRpzu3Zk7lhK4sPs7La1QnbTCbWT5kSun6utJQniovJSUmJ2aDt\nZrGQpOsszM/npv79qdc0+tnFPok8AAAgAElEQVRsHNe9O71bMJWXWqyoltXU4NP1Ni1vfLqO0+/n\n5B49cOk6fVevJs1q5fOJE6OaIXYVSikGhKVT4/OR73IxNCGhlRQbVM30sVpJMps7tVJKMJnobjZT\n5fPRz2ajl67j6sD2vSvQDGZjN5lwGPrtYQkJaFFUIk5Dfx1k+kEdvlKq3cknqLNv9PuxKUVCDKX7\nIA1VPh9Nfj8pZjMDbDZGJia2ot+j6/hFSDSZUEpRp2kUut1ktaNDt5tMjDYYq9uo+67o0DsDpRSD\nDMZf5fXS02rFYtAerprqZ7O1moTbg9PvJ9/tprfFEkqzTtNINpliukLsCN8rhj+nRw8STSb8IqFG\nCodP11lRX89bhw+TmZDAO1VVaCJUeL1c00WddUe4fu9eTECxYXc9LTWVezIyIjpolddL77Clemf0\nkbscDvY5nZzXuzf/qavj+G7duCQ9PSY0N2oafyov5+y0NA7MmEG6QVs0HWw0PF1SgqMdhv+bggJe\nqqig5oQTqPR6+bS2llpDgo0FgioNk1LoBvMJOlZpuk6lz0d3i4UUsxmfCHU+Hz3D6vyQx0OCyUSP\nNgayT9dxGBNFUJUTy8Gq6Tp1mkaG3c745GR2OBwMsNnoY7Ph8Psp93gYlpiIWSkOG34DE42J3qXr\n7HY6GZaQ0Ka0X+J2YzeZSLfZiL0xLPSwWulhtXLI0LVXeL30tVpDk2346rvS66Xa52OSQX83s5nh\nYSuDlvCLUOh208dqpZvFQrXPh0fXY6ra2e900s1QA9ZpGkUeT0B/b7GQb9RdUL9vNZkIr+Uan4/D\nXi9jkpLaHCsJSlHq9aIb5fcDA2OsEuwI3w3f9hjh9F69+E1mZps6yWKPh1O3b+eJ4cP51ZAhVJ5w\nAo2axmPFxTGjYd727Vy3Zw+PDRvGk8OHh+73sFojmL1fhIFr1/KbgoLQvd0OBwsPHqSyDXvw96qq\nOGv7di7YtQsFfDJxIiti6HhV7vFwd34+25ubMROwTYev1R4Ov58llZVAYPCevm0b74X5Trw2diyf\nteOmPrdHD24fOBClFP3sdj6dOJENU6YwPEaehmUeD1ubmwE44HJR4/MxJjk5ZNlx2OsNBUlLNpvJ\nSU2NUItU+nztbiLvdTpp9vuZkpJCg6axo7mZJk3D28kJ65VXXmnXjT7BbCYnJYUeFgu6CN0tlhCD\nFOBAQQH/MByGgpJzEHaTicF2e6twFeGhk52GF28QurEJ3Z41UDR0FDq5n81GVnIyk1NSsJhMiAgn\nnnQSayoq2HvwIFlZWaRbrQwPk/xtJhNPP/QQuV980Sq95cuXc87ZZ9Ps91PkduPWdfpYrYxOTCQz\nM5PqGEfJ1UQocLtR1dXceNllISOAcHGszueLCLinCKip2uo9SWYzwxMTGZeUxLLFi3nuV78iw9gn\naIkdO3awYMGCWBYphO8Vw4fAUrGtyIf9bDY+yc7mtLB4Fy+PHs22adNilv/01FSyU1I4rnt37iko\n4E9lZaFnFR4Pc7Zs4V1jZfHU8OGcHaZOKvF4eKa0tE1HMB1It9lYN3kyythA/W1hYcy8hUcnJeE4\n8UTO79OHpVVVDFm7lk9rv3ag/ntFBfPz8tjR3IzD2EALZyD97PZWG6Ph+FFaGhuamvhRFE/NWKC7\nxRJS6fS2WlttEmanpLQZMgFgQnIyGe1sOvez20MrMotSJJnN7DUmls6gI4YfhBDYH+lmNtPdqM9k\nk4mEw4d55403gACDDFf/mZWir83WSh3y8ccfh0Inj05Kosrno9TjoUHT2NbczHaHI+REdrQo83go\nCIs8GVSTffzxx0yeOJFRvXuH7iWElQ0C6pKFDzzArJNOipq2ydjktZtMmAhMcLE2yxyZlERfmw2L\nkVdWRgbvGBFNMxISIvpOqccTYUbay2plVFJSVM1CEMroM1aj7fq0YRE2YcIESktLKY6hIBrE94rh\nu/x+Eles4LkwJhuOZLOZzIQEHigoYK/TyduHD3PVnj3YYrjhtmjoUG4fNIgyY1CFI91mQxGQ7u0m\nE7cOGsRxYZ6Qp/bsiWv2bKa3EVP8gj59WD9lSuj5spoaXigrY3Ung651hGCHtJtMpFut2EymCOn1\n6n79+GryZCakpNDTamXdlCkRG8z7nE4eLy6mrg0G2KhpnNWrF2cZE+7odesYvHYtTxuhfY8W3SyW\n0BLfJxKwxgqjPzi4xLBhL3S7IywrOtLj97ZacRuBzbpZLPzrhRe4cuZMTp0yJRQCuKX0++STT7Jo\n0SLefvttNm7cyPz580MHarQMnfzV7t2UuN1ce801vP/OOyHaUlJSUEpxzz33hEIn//7JJyMEm4qK\nCk6cPZuJYaGTgQgJ+MEHH+SSqVO58qyzuOGKK1j6/PMMsNk47eSTQ3SMGjUq9G1XQyefOnUqhQcO\n4Pb72dbcTLlxitvixYv5yY9/zAC7HavJhN/v5+rrrmPc+PGcfvrpuFwulFJcdtVV/N0IQ/HJJ58w\nZswYZs2axbvvvgsEwlKnuVycfeaZ5EyaxB233BKxOnnttddCtPz0pz8NhYlISUnh3nvvZeLEicyc\nOZNKY5Uaji+//JKcnJyAJ/PkyVTW10e0pdPp5OKLLyZrwgQuueQSrjvlFCp37Gg3/Q8//JAZM2Yw\nadIkZp18Mivy86nz+UL+KPU+H399/XWysrKYOHEis2fPDtFzzjnn8IYxuccS3yuGn2g28+iwYcxt\nwxxye3MzX9TV8e/aWho0jVpNY5fDwa/z8yMYQyzweW0tG5qaODNsNWFWiuWTJnFRejqNmka5Yfcb\n/rwjprO8ro5/19QAsNaIJf6nUaNiQvP25mYeLiykxufjovR0XLNnc44RBRACA66tyQggz+lkYX4+\n+VFWKCJCvzVrKPB4uHXQIADO7t2bQTYbqTHQYe7/+X42z93CFuOv+LSdNM/by46Tt4XubZm7ha9m\nb2bN7M3sPWU7paftZPtJW0PPNs7ZzLrZm0LX+3/+ddx3vwgeXadB02jUNDZt2sQrr7zCxvXr+Wrd\nOl566aVQrJZouPDCC0Nu+eEHanTr1o3169dz6623cu+dd4bCHliNTb1wPPLII+QcfzwfrFvHj2++\nmUNhqr8lS5Yw/eSTeW3VKrZt20ZOTk7EtyvWreP1t99m4+bNfPDee2zZtIneVisD7HYUgTj169ev\n55lnnuG3v/0tAOnp6Xz++eds3ryZpUuXctttt7Uq14svvsjtt9/O1q1b2bZpEzNHjAjsmYiENrRX\nr17NFMPYwKFp7N+/n9OvvZYvNm+mR48evPPOO0DgYJnuFgtut5sbbriBDz/8kJUrV3Lo0CG8Ihx0\nuVi0aBGzZs0id/16Zpx5JuWGsJCXl8fSpUtZvXo1W7duxWw2h+LlOBwOZs6cybZt25g9ezYvvfRS\nq3I8/sQT3PXkk3y5cSPL/vtfGi2WCGHnhRdeILl7d15Zs4bb776bzZs2hfYbHA4H02bM4PU1a5h2\nwgmh9GfNmsW6devYsmUL5198MX975hmKPR6UUjT6/RS43Tz68MN8+umnbNu2jQ8++CCU39SpU0MT\nbyzxvdq0BfjVkCFtPnuipISV9fWUGREep3frhkvX+fmBA9w1ZAi9jtJi4ZDHw7gNG3hu5EjO7NWL\nVZMmRd1U0kX4dX4+/6+8nMPHHx9hg7yooIARiYlcEcVh67wdO8hzOkkxm/lRWhoPDxvGwzGM+Lmx\nqYn7Cgu5ql8/nIaVRc8WG4Aiwn0FBVR4vRS63bw2dmzIAemMnj1pmjUr6uazX4SHMjMjIoL+Ican\nfLl1HSFgsqdLQMpvqaAxqUC8D6tSWFtMNMEYOTZoFRitye/ngMvFmMREUiwWnlq5kuPPOosG4/Cd\nYAjgc889t0s0h4dO/sUvfhEybU02m+nRoh6VUliVolsUB59p06ZxzbXXYvX7ufSCC1ox/NWrVzP3\nrLNIMNQi55xzDmJMYkIgdDLAlClTQs5iPp+PW2+9NcRA90Xxij7uuOP43e9+R2lpKeeffz4jR44M\npJOaGpK+g6GTAao0jYGZmZw3YwZWkykiP6vJhM1kYs+ePQwdOjSU1hVXXMFzL76Iw+/n8y+/ZNl7\n75FqNnPD+efzoGHl9sUXX7Bp0yamGepZl8tFumHMYLPZOPvss0Pl+/zzz1uX44QTePyeeyi7/HIu\nv+girN270xi2n7Nq1Spuu+02Mux2uk+cyLgJE0KmpjabjXPPPpuDbjc5kyezNjcXgNLSUi655BIq\nKirwer1kDh3K6MREthAIsT3QbuekWbNYsGABF198cagNgG8sbPL3juF7jBCt0bw9H8rMpLKFuuGW\nAQO4deDAmNhRm5Vift++DE9I4L3qav5aUcHKsJC7QSyprOT/lZfzi0GDIvSYAO9VV3NC9+5RGX66\nzcaklBQWhD1bXFnJ5qammDDPa/v354q+fbEoxZwtWzjgdrNk7FhOCjMdVUqRZ2xeBu2mg2jPJd1i\nMnFhejqZ69bxt9GjY24VNfKZkaQZbdvTYqHZ78dlbO51NhRue9ZIiSYTGXZ7yIxRiWBXimqfL8I0\nMzzsMYC7g8B8bYVO9hibwSJfh04G2rQimj17NivDQiffddddEUHOEkwmelos7HQ6GW6MjUqfLxBt\nUyQU3jk8tHNXQyeffPrpPPPii1xwxhmtyqPrOiaTiQE2G6kJCSGhwGw2h06cCj8cvmU72A0GqQCT\nyYTFZMKhaegQqqerr76aRx55pBWN1rA+0DJ0dRC/uecezjv7bD7++GNmzpzJe598QlrYpniwb/Sx\n2QJOV8ZkGUzfZDIxMimJbXZ7KP2f/exn3HHHHZx77rksX76cRYsWhcaIzbCW+suf/8xXX33FsmXL\nyMnJYevWraSlpX1jYZO/VyodgPsKChj11VdRLQ8yExMp83hYkJeHput4dZ1zduxg6eHDMcm7j83G\ncyNHMrN7d7oZuvDCKAP+ovR0Xh87lieGD2/lJLZ16lReaENF89Lo0SwaOpRMoyNsamriqZISPq6N\nXWRqm+H48vPBg3H6/VGPanxz/Hg+nTiR1ZMnt2I+T5WU8GEUq4lmTUPTdRZlZIRM8ebv3s2QtWuZ\nHOUA6SNBL6uVXlYrTl1nr8uF3bDxjoYSt5t9Lc4SbW9isJtM9LJaKfF4aNI05syZw/Jly+ir63Tz\n+UIhgPv27cvhw4epqanB4/FEHF8XHjI3iGDo5NffeIPs6dNp0DSGZGSwbcsW/ESGTg5+LyIUuFwR\n1lxFRUX07tOH+ddey4Jrr2Xz5s0R+cyaNYt/L1tGmq7jd7lYtmwZiSYTvVt4kIajK6GTf/azn3HK\nvHnk7dhBo6axM+yYz2DoZAj0LwFqfb5W1k0ew+R19OjRFBQUcPDgwUDdvP46EHAcO23uXBYvXoxf\nhA8//piGujoEOOWUU3j77bc5bIzl2tpaioqK2mzPljh48CATJkxg4cKFTJg8mR15eRECzKxZs3jz\nzTcB2L1rFwd37YoQdtqqv4EDB+IX4amXX8at6yFHRRHB4fezbvduJk6bxoMPPkjv3r0pMVRU31TY\n5O8dw7+wTx9eHDWqlZuzV9dZUlnJ9uZmVjU0YDaWx5VeL0sqKzkQg4OEwyeZS/v2ZV1jI0uiTCZ2\nk4m5PXpQ7vFQ7HZHuMR3JI2+UVnJSsPMrsTtptDt5t3x44+adgiYfT5qDJIL+vSh4cQTuX7AgFbv\nBVdD+5xOHikqiij3H0tL+cjYYwjH0qoqRqxfz1X9+pFjLO9P6dmTE7p1Izs5ucumgdHgM5x5LErR\n32bDDG2GG2gMBt9qYaZY5HaHAqqFw+334za+8YowefJkFixYwCnHH89Jxx8fCgFstVq5//77mTFj\nBmeffTZjxowJpbFgwQJuuumm0KYtfB06+dlnn+WuRx/FL8IFCxawesUKLpw9OyJ0cnZ2NhaLhZyc\nHJ575hmqw+hcvnw5OZMmMWnyZN5+5x1uv/32CPp7Z2Vx8rx5nDl9Opcb+wlD0tLITExskwnccsst\nnQ6dPGnSJA4dPMgt116LR9fxGisg+Dp0cng957vd7He5Ito9KMUnJCTwl7/8hbPOOotZs2aRkZGB\nw++nyuvlgQceYMWKFUydMoWPP/2UQUOGYDeZGDduHA8//DCnn3462dnZnHbaaVR0Itx4EI899RQj\nx40je+JELAkJTD3lFNxhE9wtt9xCVVUV2dnZPPXEE4zMyqJbi9DTZR4PZWEC3qJFi7jooouYM3s2\n/fv0wScSCnToMmLq3HP33Uw2wjfPnj2biRMnAnxzYZM7E1Lz2/r7Js+03e9wCLm58opxxmkQ6xsa\nxJSbKx9XVx91Hi+Ulkq3FSuk0giZu76hIfS7Ja7Ly5N+q1ZJ71Wr5J6DB0P3/11dLZfv2tUqVO/y\nujoZsW6d9Fm5Uq7NyztqWqPhpr17ZciaNeL2+2VbU1O7oZpv3bdPctavlz6rVkWc/9pWaNmdzc3y\nRFGRNHi9HYaw7ixahond3NgoRUZY4VqvVzY0NoqjDXr8ui6eFuF4dV2XrU1NUhGlzfY4HK1CaR9w\nOmV3c7M0HWGI3LZCJzs0Tcrc7jbrSdd1ada0VuGENV2XWq+3VblERPKdTtlTXS0+XZfm5uZQ6GS3\n3x/1/ViivLxcTj311NC1z++XQx5Ph6Glg9B1PVD/DoccMMI5+40QybEKDd7g88k+hyNUp3nNzbLX\n4Qg91zQtdPbv9r17ZVBGhrhanHt82OMJ9b9oZfCGheB2apoc9njE4/e3ame32y0zZswQXxv96mjC\nI3/vdPh+Q0pLNexcg8hISGDXtGmtNrumpqaizZnT5SPPoiErOZlr+vUj2WSi3+rVLMrMZFobVi3X\n9e/PGb16UeB285MwS5hSj4d1jY3Ua1qE63ayycSUlBTuGjw4Yn8iqNZ5ZNiwNqNUdhZ/GjUKXYSd\nDgcTN27kR716cUl6OldH2U9INZs5qWdP7hg0KMI+uS09/vjkZErcbrqvXs2aSZNC5qhiSHixqP9B\nho496LKfYZzsFA0mpbAZXsQNmhYKgjWxjRAVA2w2Wq4VUs1mqnWdArc7plEPk8xmnH4/+4xAbS3r\nRoVFatR0nXKvl4F2O2alWm2yBzE0MZHzr7mGnbt3o7xeFlx9Nd3HjmWHw0G61XrUfcdhWJ0MTUho\nFe6gf//+3HDDDTQ2NtKtWzcsJlPEOBRDP+4XoVHTQnGQwss7OimJijCrNpNS2Ewm9judpHcxzEE0\ndLNYIpzwBiUkRGzcO51OTjrpJHw+Hz5d584//AGL1UqZx0MPi4XkFvwmHMHyhffF9ry0i4uLefTR\nR7HEMBJoECo44L4LmDp1qmw8An2u2+/no5oaxiYnM8Bmo9fq1Tw5fHhEoLIgHigoQAceGjoUgKvy\n8hiakMBvjetYoFHT+NXBg4xPTmaw3f6NnOoEAaugG/buZavDwUcTJrTJrLqKOp+PL+rqeLCwkLN7\n9+b3HVgCieGZOCwxkS/q6viwupqnR4yIYFSFhoPSZ3V1LOjXj/52O38sLeWOAwfob7Px1vjxET4J\nnUFeXh5jx45tdb/Y7abG52v3jOB8l4vuFgtWpdhnxNvpiGk0aBq1Ph+DExJCDjYuvx8/HHUAvkZN\n45DXS2ZCAmJc12oaIxMTW+nYfbpOvabRzWLBrescNOjvaZz1oEPUGDNOv59Gv590qxWTUtT4fDQa\nIaGPNiaN0+8PTDw2GxVeb8isdFRiYishwOn349F1elgs1GgaZR4PWcnJ6CJsczgYbLe3G2Y4iFqf\nj0ojzEVbE11X0TKEQzSICJoEQm7vcDjoa7W2Gyq73OMJBMOz2ehuRGPVjU3fWk2jm9ncrsNiS0Tr\n90qpTSLS4YHe3wsdvh+4LC+P1ysr6WGx8MqYMREerEAohk6JoTcPQgH/qavjkyh6564iqA/uZrHw\n4ujRbG1u5v/274/67gGnk1KDjgKXiwV5ea02EcMhEjhv8/nSUrYb4QO8Imxsbubp4cNjwuwfLy7m\n1UOH6Gm1cmF6OtunT++Q2UMgpPKUTZto0DS2NjfzamVlyJ48iB/v3MmioiLuycgIDY6pqanc2L8/\nJ/Xo0cpaqbMICixiDCC/CD0Mj1uPrkf1xBQJRGbUREg1mxmRkBAKKlbn83HA6YzQLesiNGkaHl2n\nye+PGDQJJhPJMQhAJnx9XOJOhwOPCKOTkqJuqHp0nSKPB7cRnjfHcISDgLd2S0/tRk1jt8OBiYC3\neTDNNKuVoYmJMQlAlmQ2MyIxkQSTKWTqmdpGULpan498txulFAmGmWlw72VsUlKribfe52OPw9Fq\nk7fYiGoZC2Zf7vGwx4jj7zIsvJra8NhXSmE1DszJSkoK9Wen4XDW0uEyxWwmzWql1OvFaZTBo+vs\ncjqp8HpDh7F3BkcroH8vJHyAHc3NjElKajP40hW7d7O6sZGCmTMj7osI3VatYuHgwfwmM/OI8g7i\njG3bcOs6uTk5mJSi1O3GD1Hd9adt2kQfq5WPs7Mp83iYsGEDfx8zhtN69uT6vXu5sE8fzg9bGZy2\nbRs9LBberqri2REj+JnhvBRLTN+0idFJSdyfkYFL19uMwOny+5m0cSP3ZmRwZb9+bGtuZmNTE1ca\nJp3RBvmH1dWYgRN79CDFbI6JCqegoIDU1FTS0tLwirDD4SDTbqe3zYZH1yOuO4tqr5fDPh+jEhND\nMZmcfj+7DXPGcOZS7fNRaKgxehkqoaOFiFCjaSQaYZ2jQTckzGh1HTRrDA+70KRpVHi9DDZUXOGx\npjy6ji7yrQbw8hmTbWfzbDDoF2OCHmSMJ7ffHzC+iMGEW+X14tD10HkOhW53RHC6cEQ7FCUYurzM\niMDasu1EBD8BCdtkqK/qNI0UI4R3Z/qOiFBTU0NTUxNDW2gkOivhf28YfjgqPB7KPB6mhunPmzWN\nKp+Pod+AbWsQr1RUoImwx+nknepq8mfMaLMh/1Nbi81kYrbhFezTdawmE7oI49av5+eDBnFTWLz4\nR4uKSDGbuTQ9nQSTKWTH7Pb7uXrPHi5OT+eCGKmOrtuzh3/X1nLzgAEIcH+LibDe5+PGfftY0K8f\n87oQWvqZkhJ+cfAgdSecEDLnDEq1R+IH4fP5KC0txW1YOjl1HbvBBBWErjvDEOo1DTNEXVrrInhE\nsKnI0MNeI7qlW9ejxkw/Gnh1nRpNIy0sgFpb8BmqgR4WC/Z23q0yTCGDoajrNY0GTcOqIsNKHwka\nNA2H33/E6WgiKAKOb7pI1DDhtT4fVpMpwjM7aKnUMnT30cKn6+gQtT4rPB7M6utT6oLhNvrZbFHb\nqq0T144ECQkJDBo0CGuL8naW4R9zy5zwv6Ox0qnxeuWhggLZ3NgoN+3dK2krV0Z975zt2+UfYZY6\n9x48KBft3HnE+UbD24cPy2/y82WfwyEvl5d3yYqjqxYsN+TlyYDVq+XFsrKuktkmdjc3y39qa+XK\n3btl/q5dnfqm0uORf1RUSL7TKf+3d698VlMTetasabKtqUlW1dfLk8XFIUuIrxoahNxc6bFypbwU\nQ/rTVq6Um/fubfP5XodDzty2TdaHHTR/0pYt8tM9e9pN91cHDsiigoKIe6Vut6xraOjUAdzt4U+l\npXLG1q3S6PPJXodDtjY2yulbt8rGKIfJb21qkudKSkJWVDVer0xYv14+qamRaq9X3q+qkpooB7j/\np7ZWXj90KHSdW1sr1+flyedhbXWkWHzokFyXlydvVVbKmdu2ydr6eum/erUsi2L99kVtbYRVXLnb\nLSo3V35fWCiX7tolw9eu7VSen9XUyCU7d8oD+flHTX8Q/6iokAt27GjX+idoIRTEAadT7jl4MHTw\nvLvFt+mrVskVu3bJo0VFUhZm2bPP4ZBF+fmytLLyqOnmWB9i/m3DBPy2qIjVDQ3cPGAAS8ePD+m7\nPLrOY8XFbGtu5rDXG3J+gMDmVrHbzXOdOLS7IzQbB09f0KcPDw0dyprGRq7fuzfq4cybm5qoMIJL\nQUD/P2fLFu6Pcgaqz1h2l7rdPFVSErEHsa6piZsGDOCnUezluwKvrvPTvXv5oq6OscnJnNKzJ/8Y\nO5bXxo3r1PcHXC6u2rOHXQ4Hb1dVscPhCD3b3NTExI0bcfj9/HLw4JDEPcRu59eDB3N6z55HHSK5\nSdPY73QG2nr4cC4zDqEpC6vjIFzGUX/hvhpfTJzIi6NHB9pv506eD+sP25ubWdvQQLnX2yp0dX+b\njampqUetVghSsrKhgdHr1+PSdT6dOJEpUTaec+vq+NmBAyGddi+rle3TpnFGr17saG7mvJ072WLs\n80BAHfjz/fs5pWdPLg0Ldje3Z09eGjOGU8PiPR0pLu/bl5fHjMEjQo3Px0C7nbPS0qJuvj5RUsID\nYf28v93Oy6NHc3nfvvxh+HDWhIX81kUYsW5dRHsE8UxpKftdLhbFwODirO3buXHvXuo0jWKPhzKv\nl2U1NVFjbJmMIINBDE9M5PfDhpGRkMAt+/Yxbv360DMRYeGQIYxITOTu/HwqwvrPiVu28MeyMt6L\ncXjndtGZWeHb+jtaO/yGNiTpA05nVBv8IH60bZucv2PHUeXt0DQhN1ceKyoK2do2+nxS5HJFlRas\ny5fL3WH29yIi9xw8KE8WF8tzJSVyaZhk/bfyckn88ktZfOiQkJsrK+rqjorWaKjxeqXvqlXyYlmZ\n/Lu6WorbsCcWCUiGw9eula1NTaF7Tk2TvObmqHbFVR6PvFVZKfsdjqiSZyzw7uHDQm6ubAmTiHus\nXCm37tvX5bR+tG2bPFlcHLq+cvduyVizptV7hzweITdXfrpnT6dtyjtCqdstrx06JLXt1JPH75dK\nj0f8LepZ13Vp8HplfUNDhA/FnQcOyPOlpVLgdEakq+u6FDqd8mVdXcx8IzqDQx5PSBruCE0+n1yT\nlydvVFZK31Wr5M9hK8EKt7tNP5eu4jf5+fJ0WJs/XVws5Oa26q/NmiZ3HzwoG8JWhyIBH4hqr1fe\nO3xYHiksbFWfuq6LU5Sjz8wAACAASURBVNMi/Gs+qKpqlc6Rgk5K+MecyYf/xcrxyqlpsryuTkrD\nlk+NPl+bTjixgEPT5PGiIvmqoUGSvvwywpmqJXRdlw+rqmRXC0eeIB4rKpIztm4NXa9raJA79u8X\nt98v9T5fK/XBPQcPyp0HDsSsHOTmyiOFhfLnsjK5OoqTx6bGRrls1y7JN5xgOosb9+yRfqtXR9zz\n+P3ijEG7FLtc8s+KCil1uSTf6RSv3y/vHT4sm6OoRKKhwu2Wc7Zvj+qAl+90yrooA9OlaXLV7t1C\nbq78p7b2qMsQDl3XZerGjfLHkpJOvb+zuVkGr1kjn7ajnhm8Zo0sCHPae6uyUsjNFXJzpfEInceC\nmL15c4cqsfZQ5/XKJzU1srOpSZ4tKYkYuyIBxn/Dnj0RqkIRkb+Ulckgw1kwlihzu+WrKKq6Urdb\nTLm58pcWKsiztm2TyRs2tErHoWlSF0Nnw7bwg2T4hS6XXLl7t3xYVSXk5kZIAyIiu5qb5aQtWyJ0\nty+Vlcn4r75qJS0dKfy6Lr8tKJDPamqk3O2WF0pLpaST0kwQXekcvy0okKkbNsh1MfK+9fn9sq6h\nQYpcLnm4sFBmb97c6W8/r6mRVysqZENDg5y5bVtoQvjYWDHk1ta2WmXZli+XnitXym1HIIlHwyc1\nNUJurqyqr2/znSWHDsmpW7dGCABuv1+y1q+P0HG3xLnbt8vL5eUR9xp9PtnU2HjUDPP2ffvkurw8\nKXS5Qh69F+zYEbHfFMSy6upWDKdZ0+SinTtlTX29fF5TI/81JqDwvvRWZaWsDFsd7nU45K79+2XJ\noUNH7W17X36+vFhWJhfv3Cn3HjwoTk2T3qtWyVNhUnMQiw8darVKXVFXJ+TmhiTr4L5Ce+NyfUOD\n3LJ3ryzIyzvq+g/ivO3b5bkOJlld11vR9a+qqlBbuTQttJL6Y0mJkJsr71ZWykMFBRF9rtDlkt8V\nFsoTRUVHTXdnGf73RocPAW/Uz2prcek6n2dn82PDg/XD6mqeLinBJ4Ej3cJ3zINecjdHCf3aFXh1\nnXqfL2TVcprhRXvL/v3sDNNnQ8CscXVDQ6uTkj6vraX7ypWhY/oC7QiHDZO0DY2NPFZcHDK9g4AD\n0ZjkZF4Oi9lyJNjR3My1e/ZQ5PEwo1s3hiQkcG9GBl9GifbZFv5RWcl9BQWYlaLc46Ha58Pt9/Pj\nnTv5Y2kpc3v2bOW1+8iwYZyTlsYJXXS6aokKj4ddDgfjkpL42+jRjElK4qDLRV6LuoeAZZDD74/w\n5rSbTOyYNo1L+/bl/epqsjdsoNY4rOKNykryXS7qNC2i7iFghz8uKalLjjPRkGQ2k2w288j/J+86\no+Moz+7dot67ZMmSLWzcsQGDTS8BTA8JLRAIxfRewkeHhN5DCb0EML2GHjCwVpdt9d7rStt7352Z\n5/uh3WXLzDYJkgP3nD1gaTQ7Ozvzzvve5z73Tk7i0I4OAMBHa9fiXJ4u57dVqrBYzgyJBB94m9du\nHx/HQ97f/1urRUlDAwZsNpxWXIyDA7Ii9kxPxyPLluGskpKoSqBouGfpUly6aBGyvJ8jRSzGGUVF\nWMPjv3PT6CjeCElp25CZidoNG3B2SQmmNm/21xUuGhzE5tZW3vf8SqfDc7OzeGXFinmdfw/Hobih\nAU9PT8NFc/JJtduNTzUa3jQzEY8c9veFhTi3tBREc7kPf/PWKH6Xl4cn9tgDYy4X7pyYCKob3TI2\nhgenpnj9tn42xPJUiPYC8BoANYCegJ/lA9gOYNj737xo+1kISodvdnzRwAAtiVD5v3d8nJY3N8/r\nfX0zyx0Gg3956WRZUjidYbOnPquVIJPReyHV+SGbja4eGqJ+q5WO6uigu8bGyMWyJJHJ6K6xMXp0\ncnJBlt982K7TUXlDA32u0dAXGk3EJfLzcjlVNjaGqY80LlcYPcNyHHVaLDRqt9Os07lgXHco7hwb\nI5FMFvT9H9neTge1tsa9rx/0ejqpq4umHA5Se3l6IWqloK6OtnR0hPnsJIoOi4W+jOLr5GFZwWuA\n4Tgattn83HazyUQXeWsMPVZrUJ2L4ziadjjoO62WtD9TbYUP8fjo/Gt2lu6bmKCdJhPl19WRLIA6\nM3k8pF0AusTOMHTZ4CB9E3Dev/Pez6ErkRG7nW4aGfF7+vjAcRzJnU7Sud30vFxOO3jqbJ6Q+laL\n2Rz0eeYD/JKUDoBDAewTMuA/AuAW7//fAuDhaPtZSPO0DouF/hPA9/2c/D3RHM/7xNQUfeotHkaS\nulk8HvrWS/kI4ZKBAXpOLicbw9Az09O002TyF35CL/C3lEo6tK1tQWipBycmCDIZWRmGPtdo/FLB\nQHyt1dJ5fX1xG1cd0tZGh7e3B/3MxjALUsjttVrpI7WaJr0cPhFRg9EYkdoJxX90Olq1c2eQdM7D\nstRjtZJSYIB62PsQfmQBluWhuGhggE6LQzL89/FxSqup4R0ApxwOQgj3POQ1FMQ8zQNVLhdl19bS\nv0LornhRbzTSD3o9jdrtdNHAQNCgOmyz0ZWDg0GGZkRzpoJlDQ20c4GKnz6YPB5qN5vDDAR/1Osp\nraYm7LqadToJMhk9HTAxmHQ4aKfJFGaE+HPgFx3w594PS0IG/EEAZd7/LwMwGG0fCzHgPyuX05k9\nPXQOj7LiTYWCDm5rC5qF/qDX057NzYIF1HgxbrfT/RMTNOVwkJVh6Knp6SA1SyyIR9P92uwsbWpp\nocPa2gSdKuOBzu323zwfqFS0f0tLzLM/k8dDD0xM0C6Tif4pl9NBra30pkLhvzm+1GrDdNlHdXRQ\nbl0dHRZHrSAS/iKgqAnENUNDdBFPgXGXyUQnd3XRUMigQkSkdbvpsLY2+iLE3ZLjOOqyWOb90Dq6\no4PuGR+nXSYTjXsHugcnJuh2nuL/c3I5faRWh/18u05Hd46NUZ/VSk9PT9OAzeZ/KFs8HvpApaLR\ngEHU5PHQfRMT9Ors7LyOX+9207VDQ/SVVktrd+2ij73HtmrnTrok5Dy7WVbwnji8vZ0ObG2lcbud\ncmpr6RO1OuJKc8Rup/8bGaFz+vrCHgSJ4Ae9nja1tPB+/9HAcRw9L5dTv9VKHpalfquVbh4ZIZFM\nRlq3m/6t0dADExNBf6N0uejhiQm6IkLPSKyIdcD/OTn8EiJSeGkjBYBivo1EItElIpGoRSQStWg0\nmnm/qZVloWcY/G3JEmxfvx4ujsPxXV1o8nrgS0WioO65XKkUlSkpuHl01O9tkwgsDAONN2nrtqoq\nLE5NhZPjcO3ICGq9/vU+qNxu7DAYgvoBfNjY0oKz+/sBzGmQmwO4/k81GjwZEvhtZBiIvVm5kRKn\nouF9tRrn9vcjNyC39vTiYuzcd9+YnQjFAG4bH0e9yYRMbwzflcPDfr72hIKCsM7cKxctwhlFRfhT\nMe/lETMG7Xb022y4urwc//RG4005nWg0mcK2TZdIeP1v9svOxmfr1mF5ejqO6+pCbl0dzu7rg4Vh\nwBCFuWUCc12WlampQW32iWBRcjLyk5Lw+54e3O/l32+pquKNsHxKLsdHPPfKUfn5uGfpUkhEItw9\nMYE6oxEbWlpwfn8/MqVSnF5cjOqAfodsqRS3V1XhwrKyeR1/XlISnly+HPtmZWF5WprfF+mckhIc\nEZIvbWIYXDsygpqQewIAXtxzT7y/ejWWpKVBe9BBSBGLkVFbixazmfd9B+x2PDI9javLy7FnenrC\nx99gMiGvvh49ViuypVJket1K31erY87JEIlEuKy8HCszMlBnMmHV7t1Yn5mJr9atQ0FSEr7T6/Hs\nzEzQ33yh1eLm8XG8o1bDs8CZ2oKI5akQywvhM3xjyO8N0fbxc/jhWxmGknfs8M86+PCdTkfL5jnL\nf8yrLpA7nWT10i6sV5sbyuG/49XT8/G+z0xP01tepcj5/f0EmYzKvFLG8/r6qDrGLsREjn/Vzp30\njVYblVe8emiIV4JGRGFLYIvH4/fLH7bZfjYO/8SurrBjumlkhNJqahLa300jI7S0qSkqVXZ4ezut\n2rmTahaoN6LGYKCuKCtCjsfL3weP199e7T3Pj05O0nsqFencbmo3m8NWgWqXiz5Vq2lgAWbIscB3\nT8TSfd5ntdKdY2NkcLvppZkZyqytDcpecLEsmTyeeVOZg97aWSCF5KNonpfLg7atNRjo2qEhMvIc\nv97tpkajkYweD72uUAQdK1F4fVHudNKPev2CyJLxW6V0QsFxHE05HAsmuxRCu9lMz0xP062joyQJ\nKR6GQuVy0Y96fdS6gkyvpysGB+mdAKkgH28u0+vpgNbWsEJSItivpYWO7ewkojm9/ZHt7WED0BsK\nBS/VwIfA81BUXx+2fLUxDE06HPPmOXebTFRrMFCzyeSvjQzYbHHr4//Y3U1nBTS9RbtuPlSpqKyh\nIahRbqHw5PQ0LW5sjLkoOeFwkEgmo9d4uPR3vZOMvpBJRuqOHSSSySL2jUTD915eu4GnXhJPQXXG\n6aSXZ2ZI7XKR3OmkQ9ra6N9eCq3eaKTrhofD7plph4MK6up45avzga92Ywihul6emaHs2lpeCuwB\nb/3L7OX/31QoFmQwjwX/CwP+owgu2j4SbR8LMeD3Wa10SFsbNfJcfFcNDdFfQhqJphwOWtrURB8u\ngJ8F0dyF+WRA4ebJ6em4vUrMHk/MA+APej1tbGmhQ9vaaHgBZmlyp9PfBdlmNtPBbW0xNy8REX2r\n0/k19ZDJgjyNPlSpwopr94yP+/105guW40i6YwfdFmXw2tjSElRcC8R9ExP0ME8Bts1spgNaW3m9\nbcbt9nmtXEweD+3Z3EwvyeW03euHQ0T0mUZDF/b3Bz3kGY6jm0dGeLutnSxLd42NUSvPMcqdTvpE\nrQ5bgb04M0MvJNArEogBm41uGhmhF2ZmaOXOnf4u7eM6O8NUUnKnkx6bmuJNhpLp9f4mNjfL0iFt\nbfRJhJW5yeOhu8fG6PSeHt6HTazwPZRuGhmhk7q6Et7PsM1G32i15GRZ/3XtG/Cfk8vpnyGrBYvH\nQ89OT9Ofe3vDGs3iRawD/oJEqohEoncBHA6gUCQSyQHcDeAhAB+IRKKtAKYAnL4Q7xUNaWIxRACv\nD3q+VOrP2fQhQyLBxqws/HNmBtlSKY5J0FdE43aDIcJBOTlBmvK/T0zgzyUlQX4lg3Y7Jp1OHJ2X\nF+am+ZZSiXMHBjCyaVOYv8zTcjnypNIgbbbPR/z1lSvn5QR65/g4gJ+CYQBg76ws1MWhwweAbpsN\n76rVuH/pUjy9bFnQ707j4elPLCiAzuOZt9ths8mEPKkUX61bh0qvY6Pa7Ua3zYYDsrP93idEhMUp\nKYKc9e1VVYLvkSGRhCVo+fT88Vgwh4Iwp0O3cxyO7urC52vX4qTCQpzsfQXCyrJ4Qi5HcXIyDgnh\nx1PEYsEgn/KUFPyBx031knl6MAHAivR0PLLHHpAZDFiXkeEPgzm9qAjukPtwyG7HX0dHsTErKyxl\na1N2NsY3bUJFSgqkYjFqA649Igq7V5wch79PTuKfy5fjwHn0cTw2PY2/T0zgjqqqICvz91QqLE1L\nwyaB1LpQLEtPxzJvLWFTdjaeW77cbwH9hU4HjghXBjjgyl0uXDkyglyJBDdXVvpdTH9WxPJU+KVe\nP2embSTo3W5atXNnmC4+Hpzf30+LGxtJ6XIFyRgtHk8YDXPzyAgl79jBu58Bm40emZzk9QjZv6WF\nTp2n548QLujvp/P7+ujFmRnqjMIhH9HeLngcQhQI49Xj/1xeOosaGsK6jYVojIXEVUNDlFlTsyCO\nh2aPh2oNhphUUULn2c2yvH8/arfzrk7ULhd9rtHMqwbBclzM1A3LcWTisQeJhssHB6k8xJZDSKYc\nL37Q6+mG4eGw/eTxeDG9o1TSDcPDgvuqNxpj7smwMwzVGQwLUtfCb9Fa4b+JWoOB3lOpaGNLCx3n\n5cCFMO1wUFOCS1C+i3vEbqd9d++O6KMSCwIN4Ijmag0HB/CoPjwxNRVmWxENGm8DUyiV4mCYOVM1\nHjOweFBvNFKNwUA1BoOftlC5XEH/jgUvzcxQbl1dzM1tdQYD7dfSMu/GPT58rFZTcX19kJQyGo7p\n6KD9W1rCfn710BAvbbappYXy6urokHnIYv8xNUUSmSzM8C1ScVkIH6hUvJLTf2s0dH+IrNGH4vr6\nedUghDAWYjZHRHTL6Cit2rlT8G/y6+oWRGYZL37TA/7Zvb10Hc9T+KiODt5i4/LmZrprgTy1P1ar\ng7Tmr8zO0tsR/Fn4YPZ4Yn7qTzgctLmlhTa1tPB298UDluNoxun0X+QGt5uOaG+nz0MG/EhwsSxd\nPDBAn4X8jYNh6GO1OqzOsN3b0ehTOM0H73nNwCKpraYcDlq5c2fY8fmww2Cgq4aGwop1n6jVtO/u\n3WHKC6K5WfJ8Zmk7TSZa2tRE7yqV9I1W66/f7DKZ6NKBgaAGvVG7nW4YHhbUin+qVgcV+X0YsNl4\na0mfazT08szMvAr+9UYj3TY6SpcPDgb1U1w5OEiF9fVB2+42meiBiQlBlc6hbW1x+Tc9NjVFp3Z3\nx3WNhsJ3vg9obaU75jkO1BuNvA/oW0dHw8YBjuNom0JBf+ju5q05xoNYB/yFj0X/H0BRUpI/ozQQ\ny9LSeBN5jsvPR63JhCemp3EDT/B5LJhwOJAiFgfFEgLAS7OzyJNKcXaAD3mjyQSGyJ92FYoVu3bh\nuPx8vBrij3Pd8DC25OfjuAAte5JIhGSxGHdUVeEwgf3FgpO6u3FaUVGQ101uUhJ+3LAhrv0kiUT4\nRq/H6hBddKpEEnZuAGBtRgbuXbIEDo5LOBuW4Tj8YDRiZVoavl+/Hku9PKyVYVBvMmGvzEz/9y4R\nibA+IwN5At4rh+Xm8p7HNLEYJcnJYQlIdpaFjWVRMQ/+NVMiwUE5OagxGvGSQgH3YYcBmOsL2C+E\nP552ufDi7Cz+UFiI5Tza81MEUs9WpKdjBc/2J4XUCBKBr271wsxMUDbxiQUFYfGeDWYzbhsfx2UC\ntYOP16zhzTd2cxySRKIwHv9puRxH5+XN63Oc3tuLCacTm7Oz/RGHwJxOXgTgxDj2LeQJ9ZlWCwfH\nBY0DAHDewAAyJRKcE/Lznw2xPBV+qdd/k9I5uatrXrP8jS0tdGxHBw3ZbEGzFzePP/yxnZ28y24f\n3lAo/G6HPjAcR3l1dYLL2vmA4zja3NpK942P0z/l8oiWD0Rzy9b/i9OO2eLxUIvZLJhZMB+ovHRR\nqApi0Gsd8FacKyyi2OWEL87MEGQy+tv4+LylvwpvetZ84GZZmnQ4wqiUVrM5KCvAB42Xw/9gHjUI\nF8vG/Nk5jiNHArz7Qa2t9LsQWw6in2TK8+Hx31Yq6dmQa4eI6OC2Njoi5D0fmpwM65gNRJfFEmbh\nHAm7TKYgK49Egd8ypfPfwDdaLf3b66PzZBR71TG7fcHMtojmLvp1u3bxXrTx4EutliCTBUknD29v\nDwoDIZozKotm8BWKOq/9bejN4GFZ6rFYaMxuT9ii18Wy1GA00vc6XRCt5WAYajQa4zIGm3U6Kau2\nNsx+WAgDNhud3t1NkMniirKMBbtNJsqtq4trAPEFwYRKaQ9vb+fl6S8ZGKD0mhpKERARxIKt3pjN\nUDAcRxaPJ67BeNBmo7vGxsK8i16bnaVtAlr7TS0t85JTCkHpcoVx+H/q7Y0YiXpBf39YcfmXwG96\nwN+mUNDSpqagG5DlOFra1MQ7KB7X2Um/X4ALxsYwtE2hCFKFfKBS0eM8nuDR9tNrtcZ8oxzW1kZ7\n7do1L5UR0dzgq3K5ggbeM3p64s7LfXhyMqyIpnW76XONxt8B6oMvNQoyWZDZXSIQGngC8aNeT0tD\n0roC4WRZum54OMwc6/GpKdpXoLvY4vGQfh6uja/NzlJ5QwN9oFIFcbmTDgddPTREPQHX03adjq4e\nGhJs2ptyOOilmZmwAbPTYuHtp2g2meiV2dl5edF8odHQU9PTtKK5mW4OWPn5vOADlVn/1mgiGs19\nr9eTSCYL8u2PhDe8GbRvzKPxysYwNGa3U1lDQ0TdfywYsdupO+TacrEsXdjfz3t9b9fpaEtHR9x1\nvlDEOuD/qvzwfShJTsaB2dlw0U8aYJ9Gnk/renReHhgiXDAwkPB7dlmtsLAsziktxaoAD/AvdDq8\nNDsbtO1nWq2gPwgAvKpQYM3u3dAEeHHPuFy4bHAQ7RZL2Pb5SUm4qrwcZyboRzPtdOKIjg7Umkwo\nTk4O8kZ/f82aoLxcIgJH4T0OgRh1ODAY4kFSkJSEkwoLURSiV8+TSvHc8uW4dfFi7JlgH4HG7caX\nWi2uKi/HZ2vXBv3uS60W3QH5rrlSKQ7KyUGOgO9QiliMfyxbFsbFFiUl8fq1OFkWs243L78cKypT\nU3FMfj7umZz0+9j7fv708uVBnvL9dju2qVSQCLzX4tRUXLxoUViW7F6ZmdibJx93U3Y2tpaVzcuL\n5sTCQlxTUYGTCwuxT8B7HJyTg0eqq5EccKxf6XR4KkJ+9KE5OXAeemiQbz8wV49hea67L3Q6TLtc\n+AtPbkCsWLZzJ24fH8fx+flB44PMYMCrCkVc+9ojLQ1rMzODfubkOHxnMGDc4Qjb/q+jo2gym3mz\nl38WxPJU+KVe/01K586xMTp7Hu3xKTt20NVDQ9TnzXX1gW/WV9bQwOvW6MOQzUbvKpVBK5Qui4VK\n6uvnZWMrhDG7nQ5pa6N/TE3RP6amIs5U5V6PkdDkp2hQOJ3UYDQueBQd0U9ZBHxKh4yaGro+gm5a\nCLHqxBuMRoJMRlv7++fNxY7b7XFJMIUw6XCEdc7+qNeHzTyJ5npQPtdo6JWZmYQtxM0eT1x0XCI2\nGtm1tbzKO87bAxCvrj8QT01P895Xlw4MUHGIyuiywcGIdJ/c6aR3lUperx0+DNhsEfOjYwV+y5TO\nfwOfqNX0kNdLIxo/P2K3z1uCGIqjOzp4b4h4cOPwMKWHmI2d09dHFwc8nPRuN909NhaX3QLRnL4d\nMhlvC3+Xl25IlAM3eTy0y2Siz9TqsFDoDoslahE6FL9rb6cjeQqEfNC63XTL6ChBJlswA7XAfWfU\n1MRdmymurw+zJa5obKQLeGIwn5XL/ZQan91BLNjU0kLHBGQw++BhWdK73XENxhzH0e2jo2ED8D+m\npsKEDD6c3dtLy36GPgiTxxM2cB/Y2kp3RhB3fOaNV+Vrcvs58Zse8M0eDy1pagpSbYzY7VTe0BDW\nREQ0lydaGcVDPRZMOhz0rlIZ1OjzrU5HN8Y5ELtZlrotlpi13Rf299PanTujZnFGA8NxYfrzW0ZH\n6e441Utfa7V0Qmdn0AAudzrpPzod7wy/oK6OIJOFFYfjxYrmZjojSmDIC97Q60gzsNdmZ+nVkBXM\nFYODdKJAncfNsnEXJwNx/fAwrWxupldnZ4P09Q6GoRuHh4P47Ofl8ogDDtFcL0jog6/NbOb1Whqx\n2+lNhcLv454ItikU9MTUFKXX1ATp4flWXs9MT0ddHWbX1kb1Q/LhW52Oju/sFPRGigaW40jvdtNr\ns7NUVF8/L08hormHRK/VGuRKOm630zl9fbweR41GI/2+q4vuGR+f1/vGOuD/KnX4mRIJDs3JCdLU\nporF2JKfjzIez5NDc3Mx5nTi0Pb2IP+OWOHiOHRarViWloY/hehpWywWvKRQ4KHqakjFYrg5Dm+r\nVDggOxsrefI+AUDj8WBdSwte2HNPP3/eaDLhFYUCD1ZXh/GzpcnJ+H1hIa6qqIj72IE5rvKO8XG8\nuWpVmH/PgyF+7AzHgQWQHIGztrEsFG43rCyLTK+mujwlRdAr5PWVK1FvMuHIBPsIBmw29Nvt+HjN\nGr93iQ8/GgwgzGWLAsCS1FQck5eHtAia/wvKysJ+tiwtze8REwiWCEMOB4qSkvyfNV5szMqCi+Ow\ndXAQr65Y4dfXp0okeCzEj6jDasUgDxccCL5+Bz7+HpjjnEO/83hxTmkpppxOyF2uIL/9VenpeHLZ\nsiDPnA80GuRIpdjKc459MB58cNC1xRLByDDIlkiQFPK9ddts2Gk246M1axI6dgPDoLChAdeUl+PU\noiLkBnyHrRYLvjcYcF1FRVj/hRCypVKsDrkOzN4M6wt46gzPzc7ie4OBtz/oZ0EsT4Vf6vXfpHRe\nm52lozs6EtJSD3v13o9NTkb11FcLaMYD4WZZ+kCl8kf1Ec05TVY0Ni44FUQ051J4ZHs7PTo5Se9G\nUQt86521xRMdSDQnt1toysMHny0tX+IXX6xiNHBev5dYZuwmj4cgk9GxnZ20ax4aeg/L0rjdHrbC\n8h1PPFC7XEHSWo7j6BO1mrc71+Lx0DdaLT05PZ3wtaXmyTJeSIzb7QQB22eiuZVpojnPFo+Hnpia\n4u1ReNqrMvKttO0MQyd3dUXs6vWwLL2lVPLujw8zTmfCVFog8FumdBKBr/iTCCweD32p1dJp3d1R\nqSGG4wRv7Pngwv5+2sLDo8aDjS0tdEKID9Bto6NB+u0Ru50emJiIu0B5w/AwZdbW8v6uz2qlH/X6\nMMlmrNC4XLTbZKI3FYoweeG43R53UeyfXl6bz8AuFCzH0auzswSZjP4xT0qKD4X19XRtiIFXNNzl\nDXT3UTROliXIZHQfT8NQvbfoDJksYS+m9Joaun5oKOz+YTiOlC5XXF5GRHP1nkDppt7tpqenpwVN\n8HxWxIlSUkJwMAzZAprEDG43rd+1K2IjH8NxJJbJotJuC43f/IB/8cAA7R2gm/5Op6Oi+nreYuPz\ncjmJZLKEBxwfOni67HaZTHTl4GDcXis9VmvMzVkPTkxQRUPDvP2AfF2QgXhpZiZuMyiF00lbOjro\nm4DC26jdLqitPrK9nVJ27KDzQrIK4oGQOVsorh8eptURzK+I5r7HRycngx7KR3V0hBVCfUjEJCwQ\nR7S30+/a2+nFmZmw2sJ9ExNBTW43Dg9HLeL2W630jVbrHwBZjqN2s5m3eK13u+kTlYq6LJaEP8Pz\ncjldOThIyTt26sIuAgAAIABJREFUBHVS883MbxoZEfQx8uFPvb0x++l0WSz0+64uum10NCGljtPb\ne3JeXx+t37Ur7r/nw5DNFrTiqDca6cyeHt4VVKfFQqd7M7jng1gH/F8lhw/MaYAXB/BiJcnJOLWo\niNd3fd+sLPypuBjHdHXhy3Xr4val1nk86LfZsCEzE+tDNLhTLhfeU6txbUUFCpOTMety4QudDicV\nFETk7c7s7cWK9HR87NWVb1MqITMa8VqIvw4ALEpJwe/y8gS90KPhhZkZvKZUonmffcJycS8O8Txx\nsCwYImRKJIIcfopYDD3DBPVBVKelBfG7gXiwuhrb9fowf/dYUW80QufxYGj//cN87htNJshdLpzh\n7VHYmJWF1Ch87Hqe73FzdjZKBTzve202pEkkCXPhpxQWotViwaVDQ9iSnx/kJRPqz99mtSI8CTkY\nKzMygupDYpEIGwQ4/LykJPxhnnnCl5WXo9ZoRKZEElTnKEpOxnPLl+OAAD+gbSoVUsXiMJ//QLy7\nenXQvx0sCyPDoCgpCdKQ707j8WCnxYI7lywJ4/djQaPJhCM7O3FbZSVWhvQijDkceEelwnmlpVgc\n4gkUCaEeR3qPBx1WK29Gx3/0enyo0WCLt8b0syOWp8Iv9fpvUjo/6vV0QmdnQjzmp9529tdnZ6Pq\nqL/zcuDROglrDIYgHvC+iQnBHNn5YptCQSd0dtLNIyNRefZ/eLN746WkdplM83YEFMLpPT20UmDW\nftHAgD8TOFZwXrVSrDLRysZG2nf3bl5b31jhZFmSO51htASbwOrB4vFQfYClhNnjofdUKl5qy8Oy\n9INOR/eMj0fNQeCDh2VpyuH4WTl8n9SRT+XiOwad250QpTPtcAj6R/3gTeDy2XX0W610XGdnVMnl\nf3S6mL2JDG43yZ3Oefsw4bdO6RDFx8u7WTbhXFW1y0Xf6XRUUl8fpFnng4tlacbp5C0wzgf3jI/P\nS1pq8XgoaceOMGnkS14Zo68pp8VspkcnJ+NePh/b2Un7CRjGjdjt9Ila7Y9WjBdKl4vqDAZ6bXY2\njDpTuVxxS+189NBTMUr9tut0VN7QQBfy6NxjQaRrdJ/du8PqKtGw22QiyGT+4mKv1UqQyXitN8ze\nonMsdBgfxry0zUtyOe/nmHY44vIyIpqbfF3Y3+9/iIzb7fS8XC64nw+8ttg98/Cn4htwmZCGrnaz\nmfZraQmL6QzF77u6aK8FoodixW9+wH9fpaKkHTv8yoRn5XLKEQgfrvUae8UbeB2KOoMh7KIbs9vp\n4oGBsCDwaBi122P2t/9IrabCujo6P8EBxweO48Iu/P/odHRhf3/chbfz+/vplgAt9aDNJjiDvHZo\niKQymaBXTSwQMg0LxZaODjo+ygDKchw9HqLcWNzYSPdG0ErPZ4aWU1tLZ/T00Ms8HZyvzM4G+duf\n1tMTdfZo9njoO53O//Bzsiz18gRy+477a62WWs3mhLqgjR4PvTwzQwe3ttLmkPxaIqLkHTv8/jpa\nt5suHhiIutLzeQvFUjTXuFz0x+5uunpoKKEanNHjoWmHgyobGwVrNPFC7XIF1WLeUSrpD93dvNfI\nuN1OW/v76cDW1oQ7nYliH/B/tRz+qvR03Lh4sZ9TXJORgfNKS5HOw/MtTU3FlYsW4cqhIbyyYkWY\nj0c0jDkcmHQ6cWhubpjHiYVl8YVOh9OLirAOQLvFggaTCVvLysI044F4ZmYGrygUsBxyCADggclJ\nGBkGj+yxR9i2ZcnJOKGgAA8myOFfOzyMGZcLH61di1BWfkt+PrYE5PEaPR4Q5rjfSEgWiSANOBeR\nvFquKC9HdWoqr797LPhQrUaORIKxTZvC6iIdFguazGZcumgRxCIRTiosDPuMoRCLRGG5CCcXFGCt\nQN9Ev80GJ8cJat2j4bqKCjSZzbh7YgIXhdRMAvXqDMeh32aDJsr1mSWV4uiA7yxFLMZqgWMXi0RB\n+QrxIkcqxUWLFiFdIoGHwjnql1aswBrv92piGHyh0+GYKHz1BWVlQb0Qeo8HVm/mgDjk/uIA7LZY\ncFpRUZhPUyx4XanEdSMj+FtVVVjdxsQweHx6GicVFITlEkRC6HEYGAbjTmfYsQNAn92OV5VKbMjM\n5D1/C45Yngq/1Ou/yeEP22x0Snd3WIdiLPDJwr7SaKLOSh6dnCTIZFF1w4M2W5DW/YrBQTozShdp\nonh4cpLO7+ujG4aHaTxKDSIRTpxobqUgxMHOF8uam+ksAR+kh7znO16OWe92x0wFHd/ZSVWNjfOS\nZToFsmh9XbzxYofB4Fd5TTsc9KZCIagUazQa6dbRUfohgRWuxeOhUbv9Z/FI8uFe7/0lVMvwsCwp\nXa6EZsjdFgu9ODPDS1GqXC4SyWR+t9ivtVr6XXs7b+pZILosFnpkcjKma87BMKRyueYtKcVvndIh\nmluuxnIiOY4jG8MkzKtPORz0qtcr5sMoy20Xy5La5Zp38HIo3lIqKau2NuHW8G+0WsqoqQkblL/X\n66m4vt7/8x/1evpXnMZpRERLmproXAHpmdzppHeUyoT9R5QuF32p1dJLMzNh59Xk8ZAioCgW63k/\nqqODDuChKPjQajbTEe3tdHACubBclGv0jJ4eWpGAT0xmba3fNC6av8vSpiZK3rEjLLA7Fnzu3ff3\nOh1vDYzPyC0a5E4n/aWvz5/73GmxhFldBKLLYonp3hMCy3G8D6zQGuDnGg0d2NoaVWL9mrcvY2wB\njPBixf/MgA9gAkA3gI5oB7WQA77c6SSRTOZ3trtueFhwZmpwu+fdOGNlGKo3GsMuBovHQ+cLeGFH\ngtrloq+12phc93qsViqoq6NTurrmla3Kh16rlS4dGIjbxfE5uTyoSNtvtQquHl7x3iDzCeG4gcf4\njQ+LGhroyhj6Cr7RaukLb9Fzxumk7NpaenMenutCmHA4CDIZXdDXR5/yqHx8mbO+4zixqyum2k69\n0eg/3zZvULzQhKbZZKJWszkhHfuUw0Gvzc6SWCbjzYtet2sX/aG7m4jmHozn9/dHXUVOOhxU1djI\nez74cG5fH53b15dQLq/C6fSH87y+QN+vnWGCvJUemJgQdMc1uN103dAQrd+1KyGVlA+xDvi/FId/\nBBFpf6H3AgDkS6W4o6oKG7y83OG5uUE+GYHIlEhwd1UVnpLLkZeUFJTrGgvaLBZYWVYwo/ZHgwEH\ne/3Vv/b6d18qkOnpw26LBSd0d6N5n32wKTsblw0OYmlaGm6urAzbNk8qxR+KinDZokUoTIDH/F1H\nB/bOzAzzbQGA1RkZeGHFCv+/FS4XksViFETh8LMkEpSnpIDhOEjFYkHfIGAu+3TbypVIEotBRHH5\nynNEeHZmBqcWFeFGnjziYbsdX+v1OLekBPlJSbiyvDwsb5cPxwbw2qliMS4sK8NyAZ39qMOBCafT\n79cTD7IkEty7ZAleUyph5biwTNrArFYnx2HW5YKT46LuN9DPP10iwbIIn3lTHPx0KBanpuLckhJY\nWBb78dQwHqquRpa3VqV2u/GDwYD/i5IbXZmaiokDDvD/e8blgpvjsFTg/A/a7TixoCChPog7xsfx\nlU6H+5cuxb4hHD4A3D0+jr0zMwWzgvkQWpuzsSzMDMO7rZll8eTMDFbNI48gLsTyVJjPC3Mz/MJY\ntv1vcvgOhqEzenroqwT85s/o6aHqxkb6UquNytud09dH1U1NUfepd7upyWj087endncHqV4WEtcN\nD9PFAwN0LU97fCgOEMgWjQSO4+htpVKwNX4+sHhlhUIpSh951Tvxzp6MXtfDWNQ3/zcyQlKZjP4a\nZ85vIDwsy8tBOxgmoVXbbpPJvxLo9lIiQjP8VrOZbhkZSSh1SeVyUX+M5ylRnNfXF1FyzHEcTToc\nvAq8aGgyGiP2TyxqaKAbvNTYM9PTdFQM9iUmj4cenJiIiaL0OdT+ajh8AOMA2gC0AriE5/eXAGgB\n0FJZWTmvDx2KwJso2gXJ530dK0btdrrd64kezXvdw7IJGz1FQpPRSCk7dsSVfxqIv42PUwXPTTXh\ncFBuXZ3fP+RzjSbuEBYHwxBkMnpQIPxZ53bTNoWCvtFq4y7+cRxHWreb/jU7Sx/z3LgOhiGd202M\nl4+N9cZ63NtgFss1MWq301+iDEpCcHuvUaEH7W2joySRyeLe70ldXbTBK3ON9llO6e6m9JqamAaz\nUNzvNa6bsNt5z+2Uw5FQfvPlg4N+u+9mk4nX1twHt9crKJJsNhIcIRSMEJ6XywUtsgOh81LEiVo2\nJ4L/pQF/kfe/xQA6ARwqtO1Cz/D3aGryp1gd39lJmwQaf4jmdNbz0bFrvA6FfBf9xQMDcSdEeViW\nPtNoYrpZGI6j3NpaOrStbUHD0YnmOMarhob8BbRY0W4206qdO6nOYCCW42jAZhPUSTd7G4Ugk/E6\nOsaC/VtaoprH+ZwtY8kY7rda6T2VihwMQzK9nlJraqj2Z3D7/MJb9Nza38+rT280GumZ6WniOI6a\nTSY6pqODBmI4R4M2m387K8PQpMMhOOkZsNmozWxOaJbeZ7XS3WNjguZrp/X00CpvF/RHajX9ubc3\nplrBUR0dYbnIQrhzbIxO6OwUzCmOhCGbjR7zKrkSbfwLhU8E4sPFAwO89Q0f/j4+Tns2NydcdCb6\nH+LwiWjW+1+1SCT6FMD+AGp/7vcFgP+rrPT7n/ypuBiOCNznvUuX4v7JSdw+Nob7Qzzgo2G7Xo8c\nqRT7C3ChvTab35/nldlZZEokYb75oSAAv+/pwT1LluDOjAxs6ezEn4qLeb3aJSIRzi0txZb8/Ihc\nOR/cHIelzc24o6oKl5eXh/0+NykJzyxf7v/3iN2OvKSkqBx+tlSK1enpSJNIIBaJsCICR7k2IwNf\nr1sHC8vy5hVEgsLlwrtqNd5cuRKlPN5ESpcL21Qq/KGwEItSUnDPkiU4MAbOOtCPpjwlBdeUl6NC\nwPto1uVCm8WCI/PykB6ht4IPK9LTcVdVFe6dnMTajAwcEJKle0BOjv9nbo6DSYALDkVg30OGRIKM\nCMcV6buJhlUZGbh40SIUJycHZe/6cGNFBSzsnPuPwuXCLoslqD9DCNvXr/f//5DdjiSRSJDDn3W5\nUJScHKajjwV/7u9HskiER6qrUcRzTT85PY0ksRhX8twbQhCJREHXAUuESFWXx6amkJ+UFLEvZ8EQ\ny1Mh0ReADABZAf/fCOBYoe3/2xGHVw8NJVSpX71zJx3R1hYT1bFh9246KYZlIdGcjYFPwnlIWxu9\nGCFLk4i/UzYa7AxDFw0M0Dm9vTGplHJqa+maOOV7ei/lshC+36GI1iXdbjYTZDL6JE6fGzvDUIfF\nEhOls02hIMhkdFpPT8J0nZCE2MEwvB470TBks9E7SiWxHEc1BkNEWWO/1Uo3Dg/HtPIJxajd/rPU\nZgJxUGtr1MjJ8QRjQ3/Q6yOu3I7t7KRTvCqja4aG6C8xulq+MDMj6N8fChvD/Dq8dABUY47G6QTQ\nC+D2SNsv9IDvZFl/wcsR5aTq3e64s099GLLZ6A/d3bQkhmJsImZYsUDndpM4Dv+XUJzY1SWok8+v\nq/Mvr99XqeIO+vANukIyOzfL0jaFgt5WKOL2XWE5joweD90zPs5rSOcLx2A4jhiOI3sEvjwQO700\n05dabVRPJo3LRX8bG6PShoaoTTmhsDIMGSPwxz5NdzQpYyieCDC5u3xwkApDwrgD8XdvY1MsYoJQ\nnNXbS0ubmgQNwGaczqjeM3x4Znrafz3WGAxR6bRlzc1++jZe6N3umB7sd42NxZwbfUhbGx0XpwfS\nfPA/MeDH+0p0wOc4jgx1hrCbZmt/P5V7tffLm5v9naocy5FbGzywnNDZGeSfHy9mnU7Bmc4to6MR\nvepZN0scG36z/KDX8xZh+bbdv6WFVu3c+bM4Ut4+OhrkyR4r9t29m+4YGyMXy9KY3S7YMWrzFnUT\nmYkTxV602xUwiAeC4zhirMEKFoPbTR+p1aRwOumlmRkSy2T+GSTrZsljXpjCu6/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MYZMAQCaSkRU60JPC/BnRtnodfrzah0AgDDRwaQIEHONTk44nKhuqUFA6vECFlCsH6XftP+raIC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SYT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\ni9c91N1XePAAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1c2b632b00>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "x = np.linspace(0, 40, 130)\n",
    "x1 = 2 * np.sin(x)\n",
    "x2 = 2 * np.cos(x)\n",
    "\n",
    "y1 = 1.6*x1**4 - 2*x2 - 10\n",
    "y2 = 1.2*x2**2 * x1 + 2*x2*3 - x1*6\n",
    "y3 = 2*x1**3 + 2*x2**3 - x1*x2\n",
    "\n",
    "plt.title(\"Discover hidden signals from observed facts\")\n",
    "l1, = plt.plot(y1, 'c:', label = 'input signals (observed facts)')\n",
    "plt.plot(y2, 'c:')\n",
    "plt.plot(y3, 'c:')\n",
    "\n",
    "l4, = plt.plot(2 * x1, 'm', label = 'output signals (hidden signals)')\n",
    "plt.plot(2 * x2, 'm') # multiplies by 2 just for visualization purpose\n",
    "\n",
    "plt.legend(handles = [l1, l4], loc = 'upper right')\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Create function that generates training samples"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 275,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "input_seq_len = 15\n",
    "output_seq_len = 20\n",
    "x = np.linspace(0, 40, 130)\n",
    "train_data_x = x[:110]\n",
    "\n",
    "def true_output_signals(x):\n",
    "    x1 = 2 * np.sin(x)\n",
    "    x2 = 2 * np.cos(x)\n",
    "    return x1, x2\n",
    "\n",
    "def true_input_signals(x):\n",
    "    x1, x2 = true_output_signals(x)\n",
    "    y1 = 1.6*x1**4 - 2*x2 - 10\n",
    "    y2 = 1.2*x2**2 * x1 + 2*x2*3 - x1*6\n",
    "    y3 = 2*x1**3 + 2*x2**3 - x1*x2\n",
    "    return y1, y2, y3\n",
    "\n",
    "def noise_func(x, noise_factor = 2):\n",
    "    return np.random.randn(len(x)) * noise_factor\n",
    "\n",
    "def generate_samples_for_output(x):\n",
    "    x1, x2 = true_output_signals(x)\n",
    "    return x1+noise_func(x1, 0.5), \\\n",
    "           x2+noise_func(x2, 0.5)\n",
    "\n",
    "def generate_samples_for_input(x):\n",
    "    y1, y2, y3 = true_input_signals(x)\n",
    "    return y1+noise_func(y1, 2), \\\n",
    "           y2+noise_func(y2, 2), \\\n",
    "           y3+noise_func(y3, 2)\n",
    "\n",
    "def generate_train_samples(x = train_data_x, batch_size = 10):\n",
    "\n",
    "    total_start_points = len(x) - input_seq_len - output_seq_len\n",
    "    start_x_idx = np.random.choice(range(total_start_points), batch_size)\n",
    "    \n",
    "    input_seq_x = [x[i:(i+input_seq_len)] for i in start_x_idx]\n",
    "    output_seq_x = [x[(i+input_seq_len):(i+input_seq_len+output_seq_len)] for i in start_x_idx]\n",
    "    \n",
    "    input_seq_y = [generate_samples_for_input(x) for x in input_seq_x]\n",
    "    output_seq_y = [generate_samples_for_output(x) for x in output_seq_x]\n",
    "    \n",
    "    ## return shape: (batch_size, time_steps, feature_dims)\n",
    "    return np.array(input_seq_y).transpose(0, 2, 1), np.array(output_seq_y).transpose(0, 2, 1)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Visualize one data sample from training"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 276,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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MDQCeFJEHELlpOwHAOxady1P8HKzseuEdbGaW1/uQyErpTstcKCJtAEoBbBSR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\nYMAnIgoIBnwiooBgwCciCggGfCKigPj/50nXH0DISnYAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1c3236c5c0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "input_seq, output_seq = generate_train_samples(batch_size=100)\n",
    "\n",
    "i1, i2, i3= plt.plot(range(input_seq_len), input_seq[0], 'yo', label = 'input_seqs_one_sample')\n",
    "o1, o2 = plt.plot(range(input_seq_len,(input_seq_len+output_seq_len)), output_seq[0], 'go', label = 'output_seqs_one_sample')\n",
    "plt.legend(handles = [i1, o1])\n",
    "plt.show()\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Build the model"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 277,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "from build_model_multi_variate import * \n",
    "\n",
    "## Parameters\n",
    "learning_rate = 0.01\n",
    "lambda_l2_reg = 0.003  \n",
    "\n",
    "## Network Parameters\n",
    "# length of input signals\n",
    "input_seq_len = 15 \n",
    "# length of output signals\n",
    "output_seq_len = 20 \n",
    "# size of LSTM Cell\n",
    "hidden_dim = 64 \n",
    "# num of input signals\n",
    "input_dim = 3 \n",
    "# num of output signals\n",
    "output_dim = 2 \n",
    "# num of stacked lstm layers \n",
    "num_stacked_layers = 2 \n",
    "# gradient clipping - to avoid gradient exploding\n",
    "GRADIENT_CLIPPING = 2.5 "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Train the model"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 278,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Training losses: \n",
      "64.2128\n",
      "28.6208\n",
      "25.0749\n",
      "25.0917\n",
      "15.6719\n",
      "10.339\n",
      "10.1405\n",
      "8.78899\n",
      "7.40599\n",
      "7.2843\n",
      "7.17353\n",
      "6.95969\n",
      "7.00498\n",
      "6.83154\n",
      "6.08503\n",
      "6.05086\n",
      "7.04767\n",
      "5.94551\n",
      "6.24737\n",
      "6.02971\n",
      "6.28249\n",
      "6.13069\n",
      "6.50115\n",
      "6.0175\n",
      "5.52102\n",
      "5.81162\n",
      "5.65957\n",
      "6.00738\n",
      "5.91883\n",
      "5.94311\n",
      "5.57701\n",
      "5.71498\n",
      "5.79946\n",
      "5.69771\n",
      "6.64276\n",
      "6.03791\n",
      "5.22044\n",
      "5.69816\n",
      "5.96274\n",
      "5.70673\n",
      "5.29704\n",
      "5.75264\n",
      "5.35655\n",
      "6.36531\n",
      "5.88117\n",
      "5.413\n",
      "5.11999\n",
      "5.61508\n",
      "5.47116\n",
      "6.1913\n",
      "6.21914\n",
      "5.6628\n",
      "5.43533\n",
      "6.43791\n",
      "5.61307\n",
      "6.06029\n",
      "5.42362\n",
      "6.00235\n",
      "5.93072\n",
      "5.51793\n",
      "6.30841\n",
      "5.38553\n",
      "5.61262\n",
      "6.00262\n",
      "5.52363\n",
      "5.93103\n",
      "5.69512\n",
      "5.32481\n",
      "6.054\n",
      "5.65259\n",
      "5.59224\n",
      "5.23299\n",
      "5.41849\n",
      "5.96831\n",
      "5.89101\n",
      "5.91692\n",
      "5.92938\n",
      "5.71318\n",
      "6.03872\n",
      "5.76452\n",
      "6.04928\n",
      "5.61834\n",
      "5.58975\n",
      "5.703\n",
      "5.61251\n",
      "5.44963\n",
      "5.26935\n",
      "6.6134\n",
      "6.0066\n",
      "5.90343\n",
      "5.2958\n",
      "5.4402\n",
      "5.62414\n",
      "5.47787\n",
      "6.48795\n",
      "5.68854\n",
      "6.0335\n",
      "5.65404\n",
      "5.30624\n",
      "5.26605\n",
      "Checkpoint saved at:  ./multivariate_ts_model0\n"
     ]
    }
   ],
   "source": [
    "total_iteractions = 100\n",
    "batch_size = 16\n",
    "KEEP_RATE = 0.5\n",
    "train_losses = []\n",
    "val_losses = []\n",
    "\n",
    "x = np.linspace(0, 40, 130)\n",
    "train_data_x = x[:110]\n",
    "\n",
    "rnn_model = build_graph(feed_previous=False)\n",
    "\n",
    "saver = tf.train.Saver()\n",
    "\n",
    "init = tf.global_variables_initializer()\n",
    "with tf.Session() as sess:\n",
    "\n",
    "    sess.run(init)\n",
    "    \n",
    "    print(\"Training losses: \")\n",
    "    for i in range(total_iteractions):\n",
    "        batch_input, batch_output = generate_train_samples(batch_size=batch_size)\n",
    "        \n",
    "        feed_dict = {rnn_model['enc_inp'][t]: batch_input[:,t] for t in range(input_seq_len)}\n",
    "        feed_dict.update({rnn_model['target_seq'][t]: batch_output[:,t] for t in range(output_seq_len)})\n",
    "        _, loss_t = sess.run([rnn_model['train_op'], rnn_model['loss']], feed_dict)\n",
    "        print(loss_t)\n",
    "        \n",
    "    temp_saver = rnn_model['saver']()\n",
    "    save_path = temp_saver.save(sess, os.path.join('./', 'multivariate_ts_model0'))\n",
    "        \n",
    "print(\"Checkpoint saved at: \", save_path)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Inference"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 280,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "INFO:tensorflow:Restoring parameters from ./multivariate_ts_model0\n"
     ]
    }
   ],
   "source": [
    "test_seq_input = np.array(generate_samples_for_input(train_data_x[-15:])).transpose(1,0)\n",
    "\n",
    "rnn_model = build_graph(feed_previous=True)\n",
    "\n",
    "init = tf.global_variables_initializer()\n",
    "with tf.Session() as sess:\n",
    "\n",
    "    sess.run(init)\n",
    "    \n",
    "    saver = rnn_model['saver']().restore(sess, os.path.join('./', 'multivariate_ts_model0'))\n",
    "    \n",
    "    feed_dict = {rnn_model['enc_inp'][t]: test_seq_input[t].reshape(1, -1) for t in range(input_seq_len)}\n",
    "    feed_dict.update({rnn_model['target_seq'][t]: np.zeros([1, output_dim], dtype=np.float32) for t in range(output_seq_len)})\n",
    "    final_preds = sess.run(rnn_model['reshaped_outputs'], feed_dict)\n",
    "    \n",
    "    final_preds = np.concatenate(final_preds, axis = 0)\n",
    "    "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Visualize predictions over true signals "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 281,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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crQ4HdXY7o81mdy69lBK7lN0mHykvL2fx4sXs3Rte7bdmhwMBmITgtMPh1vo5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\nSsUJTfhKKRUnNOErpVSc+H9B58+GhKnO6gAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1c342b50f0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "test_seq_input = np.array(generate_samples_for_input(train_data_x[-15:])).transpose(1,0)\n",
    "test_seq_output = np.array(generate_samples_for_output(train_data_x[-20:])).transpose(1,0)\n",
    "plt.title(\"Input sequence, predicted and true output sequences\")\n",
    "i1, i2, i3, = plt.plot(range(15), np.array(true_input_signals(x[95:110])).transpose(1, 0), 'c:', label = 'true input sequence')\n",
    "p1, p2 = plt.plot(range(15, 35), 4 * final_preds, 'ro', label = 'predicted outputs')\n",
    "t1, t2 = plt.plot(range(15, 35), 4 * np.array(true_output_signals(x[110:])).transpose(1, 0), 'co', alpha = 0.6, label = 'true outputs')\n",
    "plt.legend(handles = [i1, p1, t1], loc = 'upper left')\n",
    "plt.show()\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 282,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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0hMPO2DWxysqcdGPMQfwIAGOBbTGv2920eF8SkTdE5CkROTbZxkQkJCINItKw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\noVoAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1c270fdc88>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "test_seq_input = np.array(generate_samples_for_input(train_data_x[-15:])).transpose(1,0)\n",
    "test_seq_output = np.array(generate_samples_for_output(train_data_x[-20:])).transpose(1,0)\n",
    "plt.title(\"Predicted and true output sequences\")\n",
    "#i1, i2, i3, = plt.plot(range(15), np.array(true_input_signals(x[95:110])).transpose(1, 0), 'c:', label = 'true input sequence')\n",
    "p1, p2 = plt.plot(range(15, 35), final_preds, 'ro', label = 'predicted outputs')\n",
    "t1, t2 = plt.plot(range(15, 35), np.array(true_output_signals(x[110:])).transpose(1, 0), 'co', label = 'true outputs')\n",
    "plt.legend(handles = [p1, t1], loc = 'upper left')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "<a id='session3'></a>\n",
    "# Extreme events / outliers"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 283,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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1sRuTp+GXwjVOG9cwYWzlEMTnLharEXtLJIqdkzmge+xR38iN3SWDEjZ2KyhR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\n2B0Oh6PDcMLucDgcHYYTdofD4egw/h/VnoOX0QhMvAAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1c31bd0358>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "x = np.linspace(0, 60, 210)\n",
    "y = 2 * np.sin(x)\n",
    "num_events_train = 40\n",
    "num_events_test = 1\n",
    "extreme_factor = 2\n",
    "np.random.seed(10)\n",
    "train_events_x = np.random.choice(range(190), num_events_train)\n",
    "test_events_x = np.random.choice(range(190, 210), num_events_test)\n",
    "y[train_events_x] += extreme_factor\n",
    "y[test_events_x] += extreme_factor\n",
    "\n",
    "plt.title('No. of traffic v.s. days')\n",
    "\n",
    "l1, = plt.plot(x[:190], y[:190], 'y', label = 'training true signal')\n",
    "l2, = plt.plot(x[190:], y[190:], 'c--', label = 'test true signal')\n",
    "\n",
    "plt.legend(handles = [l1, l2], loc = 'upper left')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 284,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "input_seq_len = 15\n",
    "output_seq_len = 20\n",
    "extreme_factor = 2 # additional units of traffic increase if extreme / outlier\n",
    "\n",
    "x = np.linspace(0, 60, 210)\n",
    "train_data_x = x[:190]\n",
    "\n",
    "np.random.seed(10)\n",
    "num_events_train = 40 # total number of extreme events in training data\n",
    "train_events_bool = np.zeros(190)\n",
    "train_events_x = np.random.choice(range(190), num_events_train)\n",
    "train_events_bool[train_events_x] = 1\n",
    "\n",
    "num_events_test = 1 # total number of extreme events in test data \n",
    "test_events_bool = np.zeros(20)\n",
    "test_events_x = np.random.choice(range(20), num_events_test)\n",
    "test_events_bool[test_events_x] = 1.\n",
    "                    \n",
    "def true_signal(x):\n",
    "    y = 2 * np.sin(x)\n",
    "    return y\n",
    "\n",
    "def noise_func(x, noise_factor = 1):\n",
    "    return np.random.randn(len(x)) * noise_factor\n",
    "\n",
    "def generate_y_values(x, event_bool):\n",
    "    return true_signal(x) + noise_func(x) + extreme_factor * event_bool\n",
    "\n",
    "def generate_train_samples(x = train_data_x, batch_size = 10, input_seq_len = input_seq_len, output_seq_len = output_seq_len, train_events_bool = train_events_bool):\n",
    "\n",
    "    total_start_points = len(x) - input_seq_len - output_seq_len\n",
    "    start_x_idx = np.random.choice(range(total_start_points), batch_size)\n",
    "    \n",
    "    input_seq_x = [x[i:(i+input_seq_len)] for i in start_x_idx]\n",
    "    input_seq_event_bool = [train_events_bool[i:(i+input_seq_len)] for i in start_x_idx]\n",
    "    \n",
    "    output_seq_x = [x[(i+input_seq_len):(i+input_seq_len+output_seq_len)] for i in start_x_idx]\n",
    "    output_seq_event_bool = [train_events_bool[(i+input_seq_len):(i+input_seq_len+output_seq_len)] for i in start_x_idx]\n",
    "    \n",
    "    input_seq_y = [generate_y_values(x, event_bool) for x, event_bool in zip(input_seq_x, input_seq_event_bool)]\n",
    "    output_seq_y = [generate_y_values(x, event_bool) for x, event_bool in zip(output_seq_x, output_seq_event_bool)]\n",
    "    \n",
    "    #batch_x = np.array([[true_signal()]])\n",
    "    return np.array(input_seq_y), np.array(output_seq_y), np.array(input_seq_event_bool), np.array(output_seq_event_bool)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 285,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x1c28fda588>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "input_seq, output_seq, input_seq_event_bool, output_seq_event_bool = generate_train_samples(batch_size=10)\n",
    "l1, = plt.plot(range(15), input_seq[0], 'go', label = 'input sequence for one sample')\n",
    "l2, = plt.plot(range(15, 35), output_seq[0], 'ro', label = 'output sequence for one sample')\n",
    "plt.legend(handles = [l1, l2], loc = 'lower left')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 1) Using the basic univariate model"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 289,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "from build_model_basic import * \n",
    "\n",
    "## Parameters\n",
    "learning_rate = 0.01\n",
    "lambda_l2_reg = 0.003  \n",
    "\n",
    "## Network Parameters\n",
    "# length of input signals\n",
    "input_seq_len = 15 \n",
    "# length of output signals\n",
    "output_seq_len = 20 \n",
    "# size of LSTM Cell\n",
    "hidden_dim = 64 \n",
    "# num of input signals\n",
    "input_dim = 1\n",
    "# num of output signals\n",
    "output_dim = 1\n",
    "# num of stacked lstm layers \n",
    "num_stacked_layers = 2 \n",
    "# gradient clipping - to avoid gradient exploding\n",
    "GRADIENT_CLIPPING = 2.5 \n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 290,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "75.9673\n",
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      "65.5012\n",
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      "35.2429\n",
      "37.4679\n",
      "31.9065\n",
      "35.7801\n",
      "35.9545\n",
      "29.9539\n",
      "37.9872\n",
      "35.3771\n",
      "36.0521\n",
      "34.2884\n",
      "36.2329\n",
      "34.343\n",
      "Checkpoint saved at:  ./univariate_ts_model0\n"
     ]
    }
   ],
   "source": [
    "total_iteractions = 200\n",
    "batch_size = 16\n",
    "KEEP_RATE = 0.5\n",
    "train_losses = []\n",
    "val_losses = []\n",
    "\n",
    "x = np.linspace(0, 60, 210)\n",
    "train_data_x = x[:190]\n",
    "\n",
    "rnn_model = build_graph(feed_previous=False)\n",
    "\n",
    "saver = tf.train.Saver()\n",
    "\n",
    "init = tf.global_variables_initializer()\n",
    "with tf.Session() as sess:\n",
    "\n",
    "    sess.run(init)\n",
    "    \n",
    "    for i in range(total_iteractions):\n",
    "        batch_input, batch_output, input_seq_event_bool, output_seq_event_bool = generate_train_samples(batch_size=batch_size)\n",
    "        \n",
    "        feed_dict = {rnn_model['enc_inp'][t]: batch_input[:,t].reshape(-1,input_dim) for t in range(input_seq_len)}\n",
    "        feed_dict.update({rnn_model['target_seq'][t]: batch_output[:,t].reshape(-1,output_dim) for t in range(output_seq_len)})\n",
    "        _, loss_t = sess.run([rnn_model['train_op'], rnn_model['loss']], feed_dict)\n",
    "        print(loss_t)\n",
    "        \n",
    "    temp_saver = rnn_model['saver']()\n",
    "    save_path = temp_saver.save(sess, os.path.join('./', 'univariate_ts_model0'))\n",
    "        \n",
    "print(\"Checkpoint saved at: \", save_path)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Inference"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 292,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "INFO:tensorflow:Restoring parameters from ./univariate_ts_model0\n"
     ]
    }
   ],
   "source": [
    "test_seq_input = true_signal(train_data_x[-15:])\n",
    "\n",
    "rnn_model = build_graph(feed_previous=True)\n",
    "\n",
    "init = tf.global_variables_initializer()\n",
    "with tf.Session() as sess:\n",
    "\n",
    "    sess.run(init)\n",
    "    \n",
    "    saver = rnn_model['saver']().restore(sess, os.path.join('./', 'univariate_ts_model0'))\n",
    "    \n",
    "    feed_dict = {rnn_model['enc_inp'][t]: test_seq_input[t].reshape(1,1) for t in range(input_seq_len)}\n",
    "    feed_dict.update({rnn_model['target_seq'][t]: np.zeros([1, output_dim]) for t in range(output_seq_len)})\n",
    "    final_preds = sess.run(rnn_model['reshaped_outputs'], feed_dict)\n",
    "    \n",
    "    final_preds = np.concatenate(final_preds, axis = 1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 293,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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SvPbaa0yePJmpU6diZtWujoyRc47t27ezY8cOZs2aNeK9eM0VU+25Vqq9f5ES7N69W0E9\nBsyMqVOn+jrzikZgD2KuFT995JrrRSJCQT0e/P4doxHY/c61ku0jHxgA5/b2kZca3DXXi0hR27dv\np62tjba2Ng455BAOP/zwodfvv/9+yeUsX76ct956q+z3Clm/fj2PPvro0OsbbriB733ve2WXExXR\nCOx+51rp7Nx74TNr505veRj7F6lBg4Pd9PS0sHp1Az09LQwO+hvpNXXqVHp7e+nt7eXyyy/nq1/9\n6tDr/fbbr+RyxhrY9+zZk7fM0YE97qIR2MELops3QzrtPZYTVIPoI/ezf5EaMzjYTV/fElKpAcCR\nSg3Q17fEd3DP5+6772bu3Lm0tbVx5ZVXkk6n2bNnD+eddx5HH300Rx11FLfffjs//elP6e3t5eyz\nz96npZ/rvZkzZ3LzzTdzwgknsHLlShYsWEBvby8Ab731FrNnz2bXrl3cdNNNdHd309bWxs9//nMA\nXnrpJU466SSSySR33HFHRX7vaolOYPdDfeQiI/T3d5JOjzyLTad30t9f4llsGTZu3MjKlSt59tln\n6e3tZc+ePaxYsYJ169bxzjvv8NJLL7Fx40bOP//8oaCdDeLDW/r53jvggAN45plnWLx4cc7977//\n/tx44410dHTQ29vLWWedBcDLL7/M448/zpo1a7jxxhv54IMPAv/dq6U+Arv6yEVGSKVyn63mW+7H\nE088wfPPP097ezttbW089dRTvPrqq8yePZu+vj6uuuoqHnvsMQ466KAxlX/22WePabvPf/7z7Lff\nfsyYMYMpU6awbdu2MZVTi6Jxg5Jf2W6Tzk6v+6WpyQvq6k6ROpVINGW6YfZdHjTnHBdddBE333zz\nPu9t2LCBRx55hNtvv51f/OIXdHV1lV3+AQccMPR8/PjxpNNpgKLDBROJxNDzcePGFeyjj5r6aLGD\n+shFhkkml9LQMPIstqFhEslk8Gexp5xyCj/72c945513AG/0zJYtW9i2bRvOORYvXsy3vvUt1q9f\nD8DkyZPZsWNHzrIKvQfQ0tLCunXrAIb60kvZLm7qJ7CLyJDGxg5aW7tIJJoBI5FoprW1i8bG4Bs8\nRx99NN/4xjc45ZRTmDNnDgsXLmRwcJDXX3+dE088kba2Ni699FK+/e1vA3DhhRdyySWX5BwmWeg9\ngGuvvZbbbruN+fPn86c//Wlo+ac+9SlefPFFjj322BEBP66iMaWAiBS1adMmPvrRj1a7GhKQXH/P\neE0pICIiJVNgFxGJGQV2EZGYUWAXEYmZyAT2oOe1CFvU6y8i0RGJG5Sy81pkb4HOzmsBVGR4VtCi\nXn8RiZZItNjDnNeiEqJef5FShDFtb9DOPfdcfvnLXwLeGPm+vr68665atYo1a9YMvb7jjjvortHc\nx5FosYc5r0UlRL3+ElPd3YFOs5Gdthfgm9/8JgceeCDXXHNN2eUsX76c4447jkMOOWRM9dizZw/j\nx5cf2n784x8XfH/VqlVMmzaN448/HoAvf/nLY6pfGCLRYs83f0Ul5rWohKjXX2LIb/KZMgUxbS/A\nggULuPrqq5k3bx5HH3002Rsdb7jhBi677DJOPfVULrzwQvbs2cPXvvY15s6dy5w5c7jrrrsASKfT\nXHnllRx55JGcccYZQ9McZMvO/mN66KGHOO644zjmmGNYuHAhr776KnfddRff+c53aGtr49lnnx2R\nrGP9+vV84hOfYM6cOXzxi1/kvffeGyrzuuuuY+7cubS2tvLss88C3pTBH//4x2lra2POnDn09/cH\nerwj0WJPJpeO6KOGys1rUQlRr7/EUKHkMwHPozR82t7x48ezZMkSVqxYwUc+8pGhaXsB/vznP3Pw\nwQfz/e9/nx/84Ae0tbXlLC+VStHT08OqVau45JJLhoLxCy+8wNNPP83EiRNZtmwZM2bM4LnnniOV\nSnH88cezcOFC1qxZw2uvvcbGjRv54x//yJFHHsnll18+ovy33nqLK664gl//+tc0Nzfz7rvvMmXK\nFC655BKmTZvG1VdfDcDDDz88tM25555LV1cXCxYs4Otf/zo333wz3/3udwFvErTnnnuOBx98kJtu\nuolHH32UZcuWcc0113D22WeTSqUIegaASAT27AXG/v5OUqktJBJNJJNLI3PhMer1lxgKMUH78Gl7\nAXbt2sURRxzBaaedNjRt7+mnn87ChQtLKu+cc84BvPlf3n77bf76178CsGjRIiZOnAjAr371KzZt\n2sSKFSsAeO+99/jDH/7A008/zTnnnENDQwMzZ87k5JNP3qf8np4ePvnJT9Lc3AzAlClTCtZn+/bt\n7N69mwULFgBwwQUXcN555w29f+aZZwLwsY99jM2bNwMwf/58brnlFgYGBjjzzDOZPXt2Sb97qSIR\n2MELjlEOhFGvv8RMU5PX/ZJrecCCnrZ3dKLn7Ovh0/c651i2bBmf/vSnR6y7cuXKoominXNlJZMu\n1trOTg88fGrg8847j3nz5vHQQw9x6qmncvfdd3PiiSeWvM9ifPWxm9l3zOz3ZrbBzFaa2cFBVSxo\nfseRaxy6xEqIyWeCnLYXvBR5AKtXr6axsXFEQM867bTTWLZs2VAg7evrY9euXZx44omsWLGCdDrN\nG2+8wVNPPbXPtieccAKrVq1iIPOP79133y1Yr2nTprH//vsP9Z/fc889nHTSSQWPSX9/P7Nnz+aq\nq67ic5/7HBs2bCi4frn8ttgfB653zu0xs1uB64F/9F+tYPkdR65x6BI7ISafGT5tbzqdZsKECdx5\n552MGzeOiy++eKiFfOuttwJ7p+bdf//9ee655/ZJhP2hD32I+fPns2PHjrwjWS677DK2bNky1E8/\nY8YMHnjgAc466yyefPJJjjrqKFpbW3O2khsbG/nhD3/IokWLcM5x2GGH8cgjj7Bo0SIWL17M/fff\nv0+O1HvuuYcrrriCXbt2MXv27KIjbO69917uu+8+JkyYwGGHHcYtt9xS8vEsRWDT9prZF4CznHNF\nPxlhT9vb09OSJ1tMM/Pmba749iJhqIdpexcsWFDwwmqc1Mq0vRcBjwRYXmD8jiPXOHQRiZKiXTFm\n9gSQ606BTufcA5l1OoE9QN6OZzNbAiwBaKrABZpC/OZ3DDM/pIjk95vf/KbaVYiEoi1259wpzrmj\ncvxkg/oFwOeBDlegX8c51+Wca3fOtU+fPj2436AEfvM7hpkfUkTEL7+jYj6Dd7H0H5xzO4utXy1+\n8zuGmR9SxI9qpLqU4Pn9O/q6eGpmrwAJYHtm0Rrn3OUFNgGU81SkEl577TUmT57M1KlTyxqHLbXF\nOcf27dvZsWMHs2bNGvFeqRdPfQ13dM4Fe7uUiIzZzJkz2bp1K9u2bat2VcSniRMnMnPmzDFvH5k7\nT0WksAkTJuzTwpP6FInZHUVEpHQK7CIiMaPALiISM4FNKVDWTs22ATmmlivJNOCdomtVj+rnj+rn\nj+rnXy3Xsdk5V/RGoKoEdj/MbG0pw32qRfXzR/XzR/XzLwp1LEZdMSIiMaPALiISM1EM7MVTrFSX\n6ueP6ueP6udfFOpYUOT62EVEpLAotthFRKSAqgZ2M1tuZm+b2cZhy44xsx4ze8nM/o+ZfWjYe9eb\n2Stm1mdmp+Upc5aZ/dbM/mBmPzWz/XKtF3T9zOxUM1uXWb7OzD6Vp8xvmtkbZtab+Tk9pPq1mNmu\nYfu9M0+ZU8zs8czxe9zMPhxS/TqG1a3XzNJmtk+anICP3xFm9qSZbTKz35nZVZnlOY+BeW7PfAY3\nmNlxecr9WOb3eyWz/phm5BpD/Toy9dpgZs+a2TF5yv2Jmb027BiOKR3RGOp3spm9N2y/N+YpN5Dv\n8Bjqd+2wum00sw/MbEqOcgM5fhXlnKvaD3AicBywcdiy54GTMs8vAm7OPD8SeBFvNslZwKvAuBxl\n/gz4Uub5ncAVIdXvWOCwzPOjgDfylPlN4JoqHL+W4esVKPN/ANdlnl8H3BpG/UZtdzTQH8LxOxQ4\nLvN8MvBy5nOW8xgAp+NlCTPgeOC3ecp9DpiXWe8R4LMh1W8+8OHM888WqN9P8NJYhn38Tgb+rYRy\nA/kOl1u/UdueAayq5PGr5E/1KzAq4AB/YW/f/xHAv2eeX4+XODu73mPAvFFlGd6NBeMzr+cBj4VR\nvxz12A4kcrwXWGAq8/iNWK9AeX3AoZnnhwJ9VTh+3waW5ikv0OM3quwHgFPzHQPgn4Fzch2rYcsO\nBX4/7PU5wD+HUb9R636Y/I2LigSmEo7fyRQJ7JX4Do/x+N0LXBrm8Qvypxb72DcC/5B5vhjvyw9w\nOPD6sPW2ZpYNNxX4s3NuT4F1KlW/4b4IvOCcS+Up4yuZ0+Xlfro6xlC/WWb2gpk9ZWb/Kc/2jc65\nNwEyjzNCrF/W2cB9BcoI/PiZWQveWddvyX8MSvkMHp5ZXmidStVvuIspnIN4aeYY/i8zS4RYv3lm\n9qKZPWJm/zFHURX5Dpdz/MxsEvAZ4BcFigz0+AWtFgP7RcCXzWwd3unT+5nlufopRw/pKWUdv/LV\nz6uA92G9Fbgsz/Y/BD4CtAFvAv8zpPq9CTQ5544Fvgbca8OuX4So2PH7BLDTObcx18ZU4PiZ2YF4\nX+KrnXN/KbRqjmUV/wyWUb/s+p/EC+z/mGeV64H/AHwcmFJgvaDrtx7vlvhjgO8Dv8xVXI5loR4/\nvG6YZ5xz7+Z5P9DjVwk1F9idc793zi10zn0Mr9X2auatrYxs3c0E/jhq83eAg81sfIF1KlU/zGwm\nsBI43zn3ap7tB51zHzjn0sC/AHPDqJ9zLuWc2555vi6z/O9zFDFoZodmfp9DgbfDqN8wX6JAaz3o\n42dmE/C+9N3Oufszi/Mdg1I+g1szywutU6n6YWZzgLuARdm/92jOuTedJwX8GB/HsJz6Oef+4pz7\na+b5w8AEM5s2qshAv8PlHr+MYp/BwI5fpdRcYDezGZnHBuAGvIsnAA8CXzKzhJnNAv4O7yLVEOd1\ngD0JnJVZdAFev1rF62dmBwMP4V0HeKbA9ocOe/kFvK6JMOo33czGZZ4n8Y5ff44iHsQ7bhDi8Ru2\nbDGwosD2gR0/MzPgR8Am59w/DXsr3zF4EDjfPMcD72VP6bMyr3eY2fGZ8s9njMew3PqZWRNwP3Ce\nc+7lAuVmg5oB/5kxHsMx1O+QzDaY2Vy8+DPin0+Q3+Ex/H0xs4OAkwrtM6jjV1HV7ODH+6/4JvA3\nvJbOxcBVeFevXwb+O5kLbZn1O/FaeH0MG2kAPMzeESlJvID/CvC/yXEBsxL1wwtS/w/oHfYzI/Pe\nXUB75vk9wEvABrwP2KEh1e+LwO/wRhatB84YVs7w+k0F/i/wh8zjlBD/vifj5c0dXU6ljt8CvNP8\nDcP+ZqfnOwZ43QR3ZD6DL2XrlHmvd9jzdrwv+6vAD4b/jhWu313An4atuzbPd2RVpv4bgX8FDgyp\nfl8Z9hlcA8yv5He43PpltvmvwIocZQV+/Cr5oztPRURipua6YkRExB8FdhGRmFFgFxGJGQV2EZGY\nUWAXEYkZBXYRkZhRYBcRiRkFdhGRmPn/cErVVpxiSGIAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1c29689d30>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#l1, = plt.plot(range(190), true_signal(train_data_x[:190]), label = 'Training truth')\n",
    "l2, = plt.plot(range(190, 210), y[190:], 'yo', label = 'Test truth')\n",
    "l3, = plt.plot(range(190, 210), final_preds.reshape(-1), 'ro', label = 'Test predictions')\n",
    "plt.legend(handles = [l2, l3], loc = 'lower right')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 2) Using seq2seq with extreme events input to decoder"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 308,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "from build_model_with_outliers import * \n",
    "\n",
    "## Parameters\n",
    "learning_rate = 0.01\n",
    "lambda_l2_reg = 0.003  \n",
    "\n",
    "## Network Parameters\n",
    "# length of input signals\n",
    "input_seq_len = 15 \n",
    "# length of output signals\n",
    "output_seq_len = 20 \n",
    "# size of LSTM Cell\n",
    "hidden_dim = 64 \n",
    "# num of input signals\n",
    "input_dim = 1\n",
    "# num of output signals\n",
    "output_dim = 1\n",
    "# num of stacked lstm layers \n",
    "num_stacked_layers = 2 \n",
    "# gradient clipping - to avoid gradient exploding\n",
    "GRADIENT_CLIPPING = 2.5 "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 309,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "78.8276\n",
      "66.8042\n",
      "51.6649\n",
      "67.0797\n",
      "41.9553\n",
      "56.1113\n",
      "47.4071\n",
      "33.3434\n",
      "41.6836\n",
      "45.5661\n",
      "39.7866\n",
      "36.2997\n",
      "39.4818\n",
      "37.0617\n",
      "40.7857\n",
      "39.5524\n",
      "37.0894\n",
      "38.4574\n",
      "32.122\n",
      "35.256\n",
      "38.6262\n",
      "33.3138\n",
      "37.3801\n",
      "33.0894\n",
      "38.1154\n",
      "37.3743\n",
      "32.342\n",
      "36.9055\n",
      "31.2909\n",
      "33.8738\n",
      "33.4793\n",
      "32.2983\n",
      "36.9979\n",
      "39.0167\n",
      "36.3832\n",
      "32.5085\n",
      "32.487\n",
      "31.2458\n",
      "34.9322\n",
      "38.4524\n",
      "29.8378\n",
      "32.6063\n",
      "29.7634\n",
      "38.6511\n",
      "32.4908\n",
      "34.3639\n",
      "36.144\n",
      "33.8463\n",
      "33.8423\n",
      "32.6575\n",
      "27.791\n",
      "33.3984\n",
      "34.1619\n",
      "28.8376\n",
      "33.3242\n",
      "33.8179\n",
      "30.7528\n",
      "31.0163\n",
      "34.9156\n",
      "29.6787\n",
      "38.2492\n",
      "37.2946\n",
      "32.476\n",
      "29.0392\n",
      "29.7978\n",
      "32.5308\n",
      "36.8824\n",
      "28.8405\n",
      "31.0703\n",
      "30.5008\n",
      "30.6409\n",
      "27.6839\n",
      "30.3481\n",
      "32.0772\n",
      "36.5268\n",
      "31.1707\n",
      "26.9489\n",
      "32.4432\n",
      "27.8832\n",
      "26.4437\n",
      "28.9944\n",
      "27.9709\n",
      "29.1564\n",
      "29.7332\n",
      "28.1853\n",
      "28.3643\n",
      "25.9979\n",
      "29.0084\n",
      "25.7884\n",
      "21.8616\n",
      "29.6087\n",
      "29.3637\n",
      "26.4809\n",
      "24.5202\n",
      "23.5947\n",
      "26.5767\n",
      "25.7621\n",
      "24.0534\n",
      "22.5964\n",
      "25.1564\n",
      "19.7556\n",
      "22.3542\n",
      "22.2953\n",
      "24.5599\n",
      "22.8954\n",
      "24.5486\n",
      "24.0907\n",
      "24.5875\n",
      "26.2629\n",
      "25.4185\n",
      "22.5687\n",
      "23.5025\n",
      "22.8976\n",
      "23.1173\n",
      "26.4146\n",
      "22.1425\n",
      "22.9116\n",
      "24.8657\n",
      "22.4877\n",
      "20.2016\n",
      "22.2127\n",
      "23.0341\n",
      "24.4987\n",
      "20.3284\n",
      "26.0886\n",
      "22.8221\n",
      "21.083\n",
      "23.89\n",
      "22.5424\n",
      "24.8784\n",
      "26.7061\n",
      "24.5299\n",
      "25.7341\n",
      "20.1914\n",
      "22.9057\n",
      "25.4593\n",
      "23.1752\n",
      "27.0035\n",
      "23.1274\n",
      "20.7193\n",
      "28.3041\n",
      "24.2969\n",
      "22.9457\n",
      "23.2676\n",
      "22.3602\n",
      "23.5828\n",
      "28.8197\n",
      "24.8528\n",
      "23.2768\n",
      "23.3916\n",
      "24.3882\n",
      "20.2635\n",
      "24.489\n",
      "22.1174\n",
      "20.4022\n",
      "22.1901\n",
      "22.459\n",
      "24.6633\n",
      "21.9651\n",
      "22.7291\n",
      "24.0236\n",
      "24.8054\n",
      "24.1174\n",
      "21.561\n",
      "21.0226\n",
      "22.5279\n",
      "23.2571\n",
      "20.8725\n",
      "25.7456\n",
      "24.7676\n",
      "25.8831\n",
      "26.4039\n",
      "19.2642\n",
      "20.1658\n",
      "23.1132\n",
      "23.0831\n",
      "23.1122\n",
      "28.6859\n",
      "23.7312\n",
      "20.2104\n",
      "21.7893\n",
      "21.493\n",
      "19.8335\n",
      "24.0186\n",
      "22.4156\n",
      "23.0556\n",
      "23.5476\n",
      "23.0386\n",
      "25.9631\n",
      "22.11\n",
      "22.5363\n",
      "20.795\n",
      "20.8276\n",
      "22.9341\n",
      "25.7155\n",
      "22.0231\n",
      "24.7319\n",
      "20.2715\n",
      "23.4967\n",
      "24.2113\n",
      "Checkpoint saved at:  ./univariate_ts_model_eventsBool\n"
     ]
    }
   ],
   "source": [
    "total_iteractions = 200\n",
    "batch_size = 16\n",
    "KEEP_RATE = 0.5\n",
    "train_losses = []\n",
    "val_losses = []\n",
    "\n",
    "x = np.linspace(0, 60, 210)\n",
    "train_data_x = x[:190]\n",
    "\n",
    "rnn_model = build_graph(feed_previous=False)\n",
    "\n",
    "saver = tf.train.Saver()\n",
    "\n",
    "init = tf.global_variables_initializer()\n",
    "with tf.Session() as sess:\n",
    "\n",
    "    sess.run(init)\n",
    "    \n",
    "    for i in range(total_iteractions):\n",
    "        batch_input, batch_output, batch_in_event_bool, batch_out_event_bool = generate_train_samples(batch_size=batch_size)\n",
    "        \n",
    "        feed_dict = {rnn_model['enc_inp'][t]: batch_input[:,t].reshape(-1,input_dim) for t in range(input_seq_len)}\n",
    "        feed_dict.update({rnn_model['target_seq'][t]: batch_output[:,t].reshape(-1,output_dim) for t in range(output_seq_len)})\n",
    "        #feed_dict.update({rnn_model['input_seq_extremes_bool'][t]: batch_in_event_bool[:,t].reshape(-1,1) for t in range(input_seq_len)})\n",
    "        feed_dict.update({rnn_model['output_seq_extremes_bool'][t]: batch_out_event_bool[:,t].reshape(-1,1) for t in range(output_seq_len)})\n",
    "        _, loss_t = sess.run([rnn_model['train_op'], rnn_model['loss']], feed_dict)\n",
    "        print(loss_t)\n",
    "        \n",
    "    temp_saver = rnn_model['saver']()\n",
    "    save_path = temp_saver.save(sess, os.path.join('./', 'univariate_ts_model_eventsBool'))\n",
    "        \n",
    "print(\"Checkpoint saved at: \", save_path)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Inference"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 310,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "INFO:tensorflow:Restoring parameters from ./univariate_ts_model_eventsBool\n"
     ]
    }
   ],
   "source": [
    "test_seq_input = true_signal(train_data_x[-15:])\n",
    "test_events_bool_input = train_events_bool[-15:]\n",
    "test_events_bool_output = test_events_bool.copy()\n",
    "\n",
    "rnn_model = build_graph(feed_previous=True)\n",
    "\n",
    "init = tf.global_variables_initializer()\n",
    "with tf.Session() as sess:\n",
    "\n",
    "    sess.run(init)\n",
    "    \n",
    "    saver = rnn_model['saver']().restore(sess, os.path.join('./', 'univariate_ts_model_eventsBool'))\n",
    "    \n",
    "    feed_dict = {rnn_model['enc_inp'][t]: test_seq_input[t].reshape(1,1) for t in range(input_seq_len)}\n",
    "    feed_dict.update({rnn_model['target_seq'][t]: np.zeros([1, 1]) for t in range(output_seq_len)})\n",
    "    feed_dict.update({rnn_model['output_seq_extremes_bool'][t]: test_events_bool_output[t].reshape(1,1) for t in range(output_seq_len)})\n",
    "    final_preds = sess.run(rnn_model['reshaped_outputs'], feed_dict)\n",
    "    "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 311,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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KFd9QlxMcLeSyKLMPv2VmyTLGd4qZ/c7MHjOz/5ylqpJ8hkez/8ysFjgX+NEI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\n5SShqwAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1c3b91dc18>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "final_preds  = np.array(final_preds).reshape(-1)\n",
    "\n",
    "l2, = plt.plot(range(190, 210), y[190:], 'yo', label = 'Test truth')\n",
    "l3, = plt.plot(range(190, 210), final_preds.reshape(-1), 'ro', label = 'Test predictions')\n",
    "plt.legend(handles = [l2, l3], loc = 'lower right')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "<a id='session4'></a>\n",
    "# Real-world case - Beijing PM2.5 Data Set"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This data set can be downloaded from UCI website - https://archive.ics.uci.edu/ml/datasets/Beijing+PM2.5+Data\n",
    "\n",
    "The remaining session will use this dataset as an example to demonstrate on how to apply seq2seq model to solve a real world problem\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Data exploration"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 237,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "   No  year  month  day  hour  pm2.5  DEWP  TEMP    PRES cbwd    Iws  Is  Ir\n",
      "0   1  2010      1    1     0    NaN   -21 -11.0  1021.0   NW   1.79   0   0\n",
      "1   2  2010      1    1     1    NaN   -21 -12.0  1020.0   NW   4.92   0   0\n",
      "2   3  2010      1    1     2    NaN   -21 -11.0  1019.0   NW   6.71   0   0\n",
      "3   4  2010      1    1     3    NaN   -21 -14.0  1019.0   NW   9.84   0   0\n",
      "4   5  2010      1    1     4    NaN   -20 -12.0  1018.0   NW  12.97   0   0\n"
     ]
    },
    {
     "data": {
      "image/png": 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2QaGgWrVC4nby13yQoRSmVp8O57ZLH1dcVqkSvuVGvOnjSkym0bUEdflaSgm7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\nQRAEQRAO8/9NJWm53Bf4QwAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1c26437160>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import pandas as pd\n",
    "import matplotlib.pyplot as plt\n",
    "import numpy as np \n",
    "import seaborn as sns\n",
    "\n",
    "df = pd.read_csv('./PRSA_data_2010.1.1-2014.12.31.csv')\n",
    "print(df.head())\n",
    "\n",
    "cols_to_plot = [\"pm2.5\", \"DEWP\", \"TEMP\", \"PRES\", \"Iws\", \"Is\", \"Ir\"]\n",
    "i = 1\n",
    "# plot each column\n",
    "plt.figure(figsize = (10,12))\n",
    "for col in cols_to_plot:\n",
    "    plt.subplot(len(cols_to_plot), 1, i)\n",
    "    plt.plot(df[col])\n",
    "    plt.title(col, y=0.5, loc='left')\n",
    "    i += 1\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Preprocessing - there are many other ways"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 238,
   "metadata": {
    "scrolled": true
   },
   "outputs": [],
   "source": [
    "## Fill NA with 0 \n",
    "#print(df.isnull().sum())\n",
    "df.fillna(0, inplace = True)\n",
    "\n",
    "## One-hot encode 'cbwd'\n",
    "temp = pd.get_dummies(df['cbwd'], prefix='cbwd')\n",
    "df = pd.concat([df, temp], axis = 1)\n",
    "del df['cbwd'], temp\n",
    "\n",
    "## Split into train and test - I used the last 1 month data as test, but it's up to you to decide the ratio\n",
    "df_train = df.iloc[:(-31*24), :].copy()\n",
    "df_test = df.iloc[-31*24:, :].copy()\n",
    "\n",
    "## take out the useful columns for modeling - you may also keep 'hour', 'day' or 'month' and to see if that will improve your accuracy\n",
    "X_train = df_train.loc[:, ['pm2.5', 'DEWP', 'TEMP', 'PRES', 'Iws', 'Is', 'Ir', 'cbwd_NE', 'cbwd_NW', 'cbwd_SE', 'cbwd_cv']].values.copy()\n",
    "X_test = df_test.loc[:, ['pm2.5', 'DEWP', 'TEMP', 'PRES', 'Iws', 'Is', 'Ir', 'cbwd_NE', 'cbwd_NW', 'cbwd_SE', 'cbwd_cv']].values.copy()\n",
    "y_train = df_train['pm2.5'].values.copy().reshape(-1, 1)\n",
    "y_test = df_test['pm2.5'].values.copy().reshape(-1, 1)\n",
    "\n",
    "## z-score transform x - not including those one-how columns!\n",
    "for i in range(X_train.shape[1]-4):\n",
    "    temp_mean = X_train[:, i].mean()\n",
    "    temp_std = X_train[:, i].std()\n",
    "    X_train[:, i] = (X_train[:, i] - temp_mean) / temp_std\n",
    "    X_test[:, i] = (X_test[:, i] - temp_mean) / temp_std\n",
    "    \n",
    "## z-score transform y\n",
    "y_mean = y_train.mean()\n",
    "y_std = y_train.std()\n",
    "y_train = (y_train - y_mean) / y_std\n",
    "y_test = (y_test - y_mean) / y_std"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Prepare training and test datasets in 3-D format - (batch_size, time_step, feature_dim)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 243,
   "metadata": {},
   "outputs": [],
   "source": [
    "input_seq_len = 30\n",
    "output_seq_len = 5\n",
    "\n",
    "def generate_train_samples(x = X_train, y = y_train, batch_size = 10, input_seq_len = input_seq_len, output_seq_len = output_seq_len):\n",
    "\n",
    "    total_start_points = len(x) - input_seq_len - output_seq_len\n",
    "    start_x_idx = np.random.choice(range(total_start_points), batch_size, replace = False)\n",
    "    \n",
    "    input_batch_idxs = [list(range(i, i+input_seq_len)) for i in start_x_idx]\n",
    "    input_seq = np.take(x, input_batch_idxs, axis = 0)\n",
    "    \n",
    "    output_batch_idxs = [list(range(i+input_seq_len, i+input_seq_len+output_seq_len)) for i in start_x_idx]\n",
    "    output_seq = np.take(y, output_batch_idxs, axis = 0)\n",
    "    \n",
    "    return input_seq, output_seq # in shape: (batch_size, time_steps, feature_dim)\n",
    "\n",
    "def generate_test_samples(x = X_test, y = y_test, input_seq_len = input_seq_len, output_seq_len = output_seq_len):\n",
    "    \n",
    "    total_samples = x.shape[0]\n",
    "    \n",
    "    input_batch_idxs = [list(range(i, i+input_seq_len)) for i in range((total_samples-input_seq_len-output_seq_len))]\n",
    "    input_seq = np.take(x, input_batch_idxs, axis = 0)\n",
    "    \n",
    "    output_batch_idxs = [list(range(i+input_seq_len, i+input_seq_len+output_seq_len)) for i in range((total_samples-input_seq_len-output_seq_len))]\n",
    "    output_seq = np.take(y, output_batch_idxs, axis = 0)\n",
    "    \n",
    "    return input_seq, output_seq"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 244,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(10, 30, 11) (10, 5, 1)\n"
     ]
    }
   ],
   "source": [
    "x, y = generate_train_samples()\n",
    "print(x.shape, y.shape)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 245,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(709, 30, 11) (709, 5, 1)\n"
     ]
    }
   ],
   "source": [
    "test_x, test_y = generate_test_samples()\n",
    "print(test_x.shape, test_y.shape)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Building the model - same multi-variate graph"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 246,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "from tensorflow.contrib import rnn\n",
    "from tensorflow.python.ops import variable_scope\n",
    "from tensorflow.python.framework import dtypes\n",
    "import tensorflow as tf\n",
    "import copy\n",
    "import os\n",
    "\n",
    "## Parameters\n",
    "learning_rate = 0.01\n",
    "lambda_l2_reg = 0.003  \n",
    "\n",
    "## Network Parameters\n",
    "# length of input signals\n",
    "input_seq_len = input_seq_len\n",
    "# length of output signals\n",
    "output_seq_len = output_seq_len\n",
    "# size of LSTM Cell\n",
    "hidden_dim = 64 \n",
    "# num of input signals\n",
    "input_dim = X_train.shape[1]\n",
    "# num of output signals\n",
    "output_dim = y_train.shape[1]\n",
    "# num of stacked lstm layers \n",
    "num_stacked_layers = 2 \n",
    "# gradient clipping - to avoid gradient exploding\n",
    "GRADIENT_CLIPPING = 2.5 \n",
    "\n",
    "def build_graph(feed_previous = False):\n",
    "    \n",
    "    tf.reset_default_graph()\n",
    "    \n",
    "    global_step = tf.Variable(\n",
    "                  initial_value=0,\n",
    "                  name=\"global_step\",\n",
    "                  trainable=False,\n",
    "                  collections=[tf.GraphKeys.GLOBAL_STEP, tf.GraphKeys.GLOBAL_VARIABLES])\n",
    "    \n",
    "    weights = {\n",
    "        'out': tf.get_variable('Weights_out', \\\n",
    "                               shape = [hidden_dim, output_dim], \\\n",
    "                               dtype = tf.float32, \\\n",
    "                               initializer = tf.truncated_normal_initializer()),\n",
    "    }\n",
    "    biases = {\n",
    "        'out': tf.get_variable('Biases_out', \\\n",
    "                               shape = [output_dim], \\\n",
    "                               dtype = tf.float32, \\\n",
    "                               initializer = tf.constant_initializer(0.)),\n",
    "    }\n",
    "                                          \n",
    "    with tf.variable_scope('Seq2seq'):\n",
    "        # Encoder: inputs\n",
    "        enc_inp = [\n",
    "            tf.placeholder(tf.float32, shape=(None, input_dim), name=\"inp_{}\".format(t))\n",
    "               for t in range(input_seq_len)\n",
    "        ]\n",
    "\n",
    "        # Decoder: target outputs\n",
    "        target_seq = [\n",
    "            tf.placeholder(tf.float32, shape=(None, output_dim), name=\"y\".format(t))\n",
    "              for t in range(output_seq_len)\n",
    "        ]\n",
    "\n",
    "        # Give a \"GO\" token to the decoder. \n",
    "        # If dec_inp are fed into decoder as inputs, this is 'guided' training; otherwise only the \n",
    "        # first element will be fed as decoder input which is then 'un-guided'\n",
    "        dec_inp = [ tf.zeros_like(target_seq[0], dtype=tf.float32, name=\"GO\") ] + target_seq[:-1]\n",
    "\n",
    "        with tf.variable_scope('LSTMCell'): \n",
    "            cells = []\n",
    "            for i in range(num_stacked_layers):\n",
    "                with tf.variable_scope('RNN_{}'.format(i)):\n",
    "                    cells.append(tf.contrib.rnn.LSTMCell(hidden_dim))\n",
    "            cell = tf.contrib.rnn.MultiRNNCell(cells)\n",
    "         \n",
    "        def _rnn_decoder(decoder_inputs,\n",
    "                        initial_state,\n",
    "                        cell,\n",
    "                        loop_function=None,\n",
    "                        scope=None):\n",
    "          \"\"\"RNN decoder for the sequence-to-sequence model.\n",
    "          Args:\n",
    "            decoder_inputs: A list of 2D Tensors [batch_size x input_size].\n",
    "            initial_state: 2D Tensor with shape [batch_size x cell.state_size].\n",
    "            cell: rnn_cell.RNNCell defining the cell function and size.\n",
    "            loop_function: If not None, this function will be applied to the i-th output\n",
    "              in order to generate the i+1-st input, and decoder_inputs will be ignored,\n",
    "              except for the first element (\"GO\" symbol). This can be used for decoding,\n",
    "              but also for training to emulate http://arxiv.org/abs/1506.03099.\n",
    "              Signature -- loop_function(prev, i) = next\n",
    "                * prev is a 2D Tensor of shape [batch_size x output_size],\n",
    "                * i is an integer, the step number (when advanced control is needed),\n",
    "                * next is a 2D Tensor of shape [batch_size x input_size].\n",
    "            scope: VariableScope for the created subgraph; defaults to \"rnn_decoder\".\n",
    "          Returns:\n",
    "            A tuple of the form (outputs, state), where:\n",
    "              outputs: A list of the same length as decoder_inputs of 2D Tensors with\n",
    "                shape [batch_size x output_size] containing generated outputs.\n",
    "              state: The state of each cell at the final time-step.\n",
    "                It is a 2D Tensor of shape [batch_size x cell.state_size].\n",
    "                (Note that in some cases, like basic RNN cell or GRU cell, outputs and\n",
    "                 states can be the same. They are different for LSTM cells though.)\n",
    "          \"\"\"\n",
    "          with variable_scope.variable_scope(scope or \"rnn_decoder\"):\n",
    "            state = initial_state\n",
    "            outputs = []\n",
    "            prev = None\n",
    "            for i, inp in enumerate(decoder_inputs):\n",
    "              if loop_function is not None and prev is not None:\n",
    "                with variable_scope.variable_scope(\"loop_function\", reuse=True):\n",
    "                  inp = loop_function(prev, i)\n",
    "              if i > 0:\n",
    "                variable_scope.get_variable_scope().reuse_variables()\n",
    "              output, state = cell(inp, state)\n",
    "              outputs.append(output)\n",
    "              if loop_function is not None:\n",
    "                prev = output\n",
    "          return outputs, state\n",
    "\n",
    "        def _basic_rnn_seq2seq(encoder_inputs,\n",
    "                              decoder_inputs,\n",
    "                              cell,\n",
    "                              feed_previous,\n",
    "                              dtype=dtypes.float32,\n",
    "                              scope=None):\n",
    "          \"\"\"Basic RNN sequence-to-sequence model.\n",
    "          This model first runs an RNN to encode encoder_inputs into a state vector,\n",
    "          then runs decoder, initialized with the last encoder state, on decoder_inputs.\n",
    "          Encoder and decoder use the same RNN cell type, but don't share parameters.\n",
    "          Args:\n",
    "            encoder_inputs: A list of 2D Tensors [batch_size x input_size].\n",
    "            decoder_inputs: A list of 2D Tensors [batch_size x input_size].\n",
    "            feed_previous: Boolean; if True, only the first of decoder_inputs will be\n",
    "              used (the \"GO\" symbol), all other inputs will be generated by the previous \n",
    "              decoder output using _loop_function below. If False, decoder_inputs are used \n",
    "              as given (the standard decoder case).\n",
    "            dtype: The dtype of the initial state of the RNN cell (default: tf.float32).\n",
    "            scope: VariableScope for the created subgraph; default: \"basic_rnn_seq2seq\".\n",
    "          Returns:\n",
    "            A tuple of the form (outputs, state), where:\n",
    "              outputs: A list of the same length as decoder_inputs of 2D Tensors with\n",
    "                shape [batch_size x output_size] containing the generated outputs.\n",
    "              state: The state of each decoder cell in the final time-step.\n",
    "                It is a 2D Tensor of shape [batch_size x cell.state_size].\n",
    "          \"\"\"\n",
    "          with variable_scope.variable_scope(scope or \"basic_rnn_seq2seq\"):\n",
    "            enc_cell = copy.deepcopy(cell)\n",
    "            _, enc_state = rnn.static_rnn(enc_cell, encoder_inputs, dtype=dtype)\n",
    "            if feed_previous:\n",
    "                return _rnn_decoder(decoder_inputs, enc_state, cell, _loop_function)\n",
    "            else:\n",
    "                return _rnn_decoder(decoder_inputs, enc_state, cell)\n",
    "\n",
    "        def _loop_function(prev, _):\n",
    "          '''Naive implementation of loop function for _rnn_decoder. Transform prev from \n",
    "          dimension [batch_size x hidden_dim] to [batch_size x output_dim], which will be\n",
    "          used as decoder input of next time step '''\n",
    "          return tf.matmul(prev, weights['out']) + biases['out']\n",
    "        \n",
    "        dec_outputs, dec_memory = _basic_rnn_seq2seq(\n",
    "            enc_inp, \n",
    "            dec_inp, \n",
    "            cell, \n",
    "            feed_previous = feed_previous\n",
    "        )\n",
    "\n",
    "        reshaped_outputs = [tf.matmul(i, weights['out']) + biases['out'] for i in dec_outputs]\n",
    "        \n",
    "    # Training loss and optimizer\n",
    "    with tf.variable_scope('Loss'):\n",
    "        # L2 loss\n",
    "        output_loss = 0\n",
    "        for _y, _Y in zip(reshaped_outputs, target_seq):\n",
    "            output_loss += tf.reduce_mean(tf.pow(_y - _Y, 2))\n",
    "\n",
    "        # L2 regularization for weights and biases\n",
    "        reg_loss = 0\n",
    "        for tf_var in tf.trainable_variables():\n",
    "            if 'Biases_' in tf_var.name or 'Weights_' in tf_var.name:\n",
    "                reg_loss += tf.reduce_mean(tf.nn.l2_loss(tf_var))\n",
    "\n",
    "        loss = output_loss + lambda_l2_reg * reg_loss\n",
    "\n",
    "    with tf.variable_scope('Optimizer'):\n",
    "        optimizer = tf.contrib.layers.optimize_loss(\n",
    "                loss=loss,\n",
    "                learning_rate=learning_rate,\n",
    "                global_step=global_step,\n",
    "                optimizer='Adam',\n",
    "                clip_gradients=GRADIENT_CLIPPING)\n",
    "        \n",
    "    saver = tf.train.Saver\n",
    "    \n",
    "    return dict(\n",
    "        enc_inp = enc_inp, \n",
    "        target_seq = target_seq, \n",
    "        train_op = optimizer, \n",
    "        loss=loss,\n",
    "        saver = saver, \n",
    "        reshaped_outputs = reshaped_outputs,\n",
    "        )"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Train the model "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 247,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Training losses: \n",
      "12.7415\n",
      "49.3645\n",
      "11.9952\n",
      "19.3026\n",
      "2.27891\n",
      "10.0695\n",
      "6.88179\n",
      "1.61318\n",
      "3.43801\n",
      "1.48012\n",
      "2.08897\n",
      "2.23086\n",
      "1.14729\n",
      "1.24911\n",
      "1.19186\n",
      "0.825225\n",
      "1.39854\n",
      "0.83422\n",
      "0.993482\n",
      "1.15438\n",
      "0.91724\n",
      "0.449349\n",
      "0.342243\n",
      "0.773666\n",
      "3.1517\n",
      "0.742146\n",
      "0.726734\n",
      "0.693751\n",
      "0.72849\n",
      "3.75605\n",
      "0.781623\n",
      "0.435807\n",
      "0.638508\n",
      "0.323507\n",
      "0.731374\n",
      "5.73397\n",
      "0.957414\n",
      "0.566127\n",
      "1.117\n",
      "1.61221\n",
      "1.45885\n",
      "0.476478\n",
      "0.395423\n",
      "0.386837\n",
      "0.668713\n",
      "0.498765\n",
      "0.371423\n",
      "0.292672\n",
      "0.759234\n",
      "1.33207\n",
      "0.278139\n",
      "0.709335\n",
      "2.95788\n",
      "0.376149\n",
      "0.526011\n",
      "0.525355\n",
      "0.908295\n",
      "0.91461\n",
      "0.275369\n",
      "0.94319\n",
      "0.355082\n",
      "0.270793\n",
      "3.21877\n",
      "0.470822\n",
      "0.27784\n",
      "0.51771\n",
      "0.296252\n",
      "0.485652\n",
      "0.387177\n",
      "0.234737\n",
      "0.528883\n",
      "0.464315\n",
      "0.873771\n",
      "0.320562\n",
      "0.398915\n",
      "0.18107\n",
      "0.317256\n",
      "0.642497\n",
      "0.332196\n",
      "0.340152\n",
      "0.374909\n",
      "0.248349\n",
      "0.421241\n",
      "0.195085\n",
      "0.984978\n",
      "0.277065\n",
      "0.240515\n",
      "0.463023\n",
      "0.624892\n",
      "0.475202\n",
      "0.643531\n",
      "0.551283\n",
      "0.176235\n",
      "0.770045\n",
      "0.35904\n",
      "0.224581\n",
      "0.498367\n",
      "0.342903\n",
      "0.263045\n",
      "0.169285\n",
      "Checkpoint saved at:  ./multivariate_ts_pollution_case\n"
     ]
    }
   ],
   "source": [
    "total_iteractions = 100\n",
    "batch_size = 16\n",
    "KEEP_RATE = 0.5\n",
    "train_losses = []\n",
    "val_losses = []\n",
    "\n",
    "x = np.linspace(0, 40, 130)\n",
    "train_data_x = x[:110]\n",
    "\n",
    "rnn_model = build_graph(feed_previous=False)\n",
    "\n",
    "saver = tf.train.Saver()\n",
    "\n",
    "init = tf.global_variables_initializer()\n",
    "with tf.Session() as sess:\n",
    "\n",
    "    sess.run(init)\n",
    "    \n",
    "    print(\"Training losses: \")\n",
    "    for i in range(total_iteractions):\n",
    "        batch_input, batch_output = generate_train_samples(batch_size=batch_size)\n",
    "        \n",
    "        feed_dict = {rnn_model['enc_inp'][t]: batch_input[:,t] for t in range(input_seq_len)}\n",
    "        feed_dict.update({rnn_model['target_seq'][t]: batch_output[:,t] for t in range(output_seq_len)})\n",
    "        _, loss_t = sess.run([rnn_model['train_op'], rnn_model['loss']], feed_dict)\n",
    "        print(loss_t)\n",
    "        \n",
    "    temp_saver = rnn_model['saver']()\n",
    "    save_path = temp_saver.save(sess, os.path.join('./', 'multivariate_ts_pollution_case'))\n",
    "        \n",
    "print(\"Checkpoint saved at: \", save_path)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Inference on test \n",
    "Notice the batch prediction which is different to previous"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 248,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "INFO:tensorflow:Restoring parameters from ./multivariate_ts_pollution_case\n",
      "Test mse is:  0.336378205965\n"
     ]
    }
   ],
   "source": [
    "rnn_model = build_graph(feed_previous=True)\n",
    "\n",
    "init = tf.global_variables_initializer()\n",
    "with tf.Session() as sess:\n",
    "\n",
    "    sess.run(init)\n",
    "    \n",
    "    saver = rnn_model['saver']().restore(sess,  os.path.join('./', 'multivariate_ts_pollution_case'))\n",
    "    \n",
    "    feed_dict = {rnn_model['enc_inp'][t]: test_x[:, t, :] for t in range(input_seq_len)} # batch prediction\n",
    "    feed_dict.update({rnn_model['target_seq'][t]: np.zeros([test_x.shape[0], output_dim], dtype=np.float32) for t in range(output_seq_len)})\n",
    "    final_preds = sess.run(rnn_model['reshaped_outputs'], feed_dict)\n",
    "    \n",
    "    final_preds = [np.expand_dims(pred, 1) for pred in final_preds]\n",
    "    final_preds = np.concatenate(final_preds, axis = 1)\n",
    "    print(\"Test mse is: \", np.mean((final_preds - test_y)**2))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 312,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "## remove duplicate hours and concatenate into one long array\n",
    "test_y_expand = np.concatenate([test_y[i].reshape(-1) for i in range(0, test_y.shape[0], 5)], axis = 0)\n",
    "final_preds_expand = np.concatenate([final_preds[i].reshape(-1) for i in range(0, final_preds.shape[0], 5)], axis = 0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 258,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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liUQ6l9jNc2kxnjgyGWXFhAMZ0jlDflMkmzVeGT+3RewUK3rs1a0YFUFjEXsH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\nTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1c2b9dc2b0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(final_preds_expand, color = 'orange', label = 'predicted')\n",
    "plt.plot(test_y_expand, color = 'blue', label = 'actual')\n",
    "plt.title(\"test data - one month\")\n",
    "plt.legend(loc=\"upper left\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python [conda root]",
   "language": "python",
   "name": "conda-root-py"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.5.4"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}
